Amenability of Hopf C^*-algebras
Chi-Keung Ng
给出了一般Hopf C^*-代数顺从性的三个自然定义（它们都是局部紧群情形的推广），并研究了它们之间的关系.此外，还研究了Hopf C^*-代数在对偶情形下的顺从性.
Three natural definitions for amenability of general Hopf C^*-algebras (all of them being generalizations of the case of locally compact groups) were given and the relations between them were studied. Moreover, amenability in the situation of duality of Hopf C^*-algebras was also studied.
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Amenability and exactness for dynamical systems and their C*-algebras
在这项调查中，我们研究了顺从性（分别）之间的关系。C*-动力系统在无穷远处的可顺应性（amenability at infinity）和相等性（equality）或核性（nuclearity）（resp.精确度）的相应交叉产品。
A characterization of amenability of group actions on $C^\ast$-algebras
我们证明了当一个群作用在一个有单位元的交换$C^\ast$ -代数上时，它的全积和约化交叉积$C^\ast$ -代数的重合性意味着该作用的顺从性.这是对C. 1987年的Anantharaman-Delaroche。
We study some general properties of tracial C*-algebras. In the first part, we consider Dixmier type approximation theorem and characterize symmetric amenability for C*-algebras. In the second part, we consider continuous bundles of tracial von Neumann algebras and classify some of them.
Amenability of the Algebras R(S), F(S) of a Topological Semigroup S
对于局部紧Hausdorff半群S，Dunkl和Ramirez对$L^\infty$表示代数R（S）进行了广泛的研究. Lau研究了拓扑半群的Fourier-Stieltjes代数F（S）。本文的目的是研究这两个代数，并研究它们关于S的结构的顺从性。
In this work we apply Noncommutative Potential Theory to prove (relative) amenability and the (relative) Haagerup Property $(H)$ of von Neumann algebras in terms of the spectral growth of Dirichlet forms. Examples deal with (inclusions of) countable discrete groups and free orthogonal compact quantum groups.
Semigroup C*-algebras and amenability of semigroups
构造了左可消半群的约化和满半群C* 代数.我们的新结构涵盖了A.尼卡也Toeplitz代数重视环的整数在一些领域由于J.坎茨。此外，我们还证明了半群的（左）顺从性可以用这些半群C* 代数来表示，类似于群的情况。
We generalize Renault's notion of measurewise amenability to actions of second countable, Hausdorff, étale groupoids on separable $C^*$-algebras and show that measurewise amenability characterizes nuclearity of the crossed product whenever the $C^*$-algebra acted on is nuclear. In the more general context of Fell bundles over second countable, Hausdorff, étale groupoids, we introduce a version of Exel's approximation property. We prove that the approximation property implies nuclearity of the cross-sectional algebra whenever the unit bundle is nuclear. For Fell bundles associated to groupoid a…
Essential groupoid amenability and nuclearity of groupoid C*-algebras
本文构造了étale群胚的本质C*-代数，引入其极大版本及本质顺从性条件（弱于拓扑顺从性），并将可消半群代数作用产生的Bruce-Li代数描述为奇异本质C*-代数。
Nuclearity of semigroup C*-algebras and the connection to amenability
研究了与群的子半群相关联的C* 代数。对于一类包含拟格序群中的正锥的半群和左Ore半群，我们将相应的半群C* 代数-代数刻画为逆半群的C* 代数-代数、群胚C* 代数-代数和群交叉积的全角.这些描述使我们能够用左正则表示的忠实性和群作用的顺从性来刻画半群C* 代数的核性。此外，我们还确定了半群C* 代数的边界元何时是UCT Kirchberg代数.这导致了Cuntz代数和环C* 代数的统一方法。
We prove a functoriality result for the full C*-algebras of right-LCM monoids with respect to monoid inclusions that are closed under factorization and preserve orthogonality, and use this to show that if a right-LCM monoid is amenable in the sense of Nica, then so are its submonoids. As applications, we complete the classification of Artin monoids with respect to Nica amenability by showing that only the right-angled ones are amenable in the sense of Nica and we show that the Nica amenability of a graph product of right-LCM semigroups is inherited by the factors.
In this article, we give explicit examples of maximal amenable subalgebras of the $q$-Gaussian algebras, namely, the generator subalgebra is maximal amenable inside the $q$-Gaussian algebras for real numbers $q$ with its absolute value sufficiently small. To achieve this, we construct a Riesz basis in the spirit of Rădulescu and develop a structural theorem for the $q$-Gaussian algebras.
We recast the Foelner condition in an operator algebraic setting and prove that it implies a certain dimension flatness property. Furthermore, it is proven that the Foelner condition generalizes the existing notions of amenability and that the enveloping von Neumann algebra arising from a Foelner algebra is automatically injective. As an application we show how our techniques unify the previously known results concerning vanishing of L^2-Betti numbers for amenable groups, groupoids and quantum groups and moreover provides a large class of new examples of algebras with vanishing L^2-Betti numbe…
In this paper, we give another two characterizations of relative amenability on finite von Neumann algebras, one of which can be thought of as an analogue of injective operator systems. As an application, we prove a stable property of relative amenable inclusions. We prove that under certain assumptions, the inclusion $N=\int_{X} \bigoplus N_{p} d μ\subset M=\int_{X} \bigoplus M_{p} d μ$ is amenable if and only if $N_p\subset M_p$ is amenable almost everywhere.
Amenability and Uniqueness
本文的主要结果是利用唯一性定理刻画了真无限内射von Neumann代数和核C* 代数-代数，并推广了Voiculescu著名的Weyl-von Neumann定理.
$C^*$-algebras of inverse semigroups: amenability and weak containment
我们认为，弱包含是逆半群的顺从性的一个适当的概念。给定逆半群$S$和$S$到群$G$上的同态$ϕ$，在对$\ker(ϕ)$的一个假设下，我们证明了$S$有弱包含当且仅当$G$顺从且$\ker(ϕ)$有弱包含.利用Fell丛顺从性，我们得到了含零逆半群的一个相关结果。证明了所有的图逆半群都有弱包含性，并且证明了拟格序群$(G,P)$的Nica逆半群$\mcT_{G,P}$有弱包含性当且仅当$(G,P)$顺从.
We investigate recent uniqueness theorems for reduced $C^*$-algebras of Hausdorff étale groupoids in the context of inverse semigroups. In many cases the distinguished subalgebra is closely related to the structure of the inverse semigroup. In order to apply our results to full $C^*$-algebras, we also investigate amenability. More specifically, we obtain conditions that guarantee amenability of the universal groupoid for certain classes of inverse semigroups. These conditions also imply the existence of a conditional expectation onto a canonical subalgebra.
Amenability and weak amenability of the Fourier algebra
设$G$是一个局部紧群.证明了它的Fourier代数$A(G)$是顺从的当且仅当$G$有有限指标的阿贝尔子群，它的Fourier-Stieltjes代数$B(G)$是顺从的当且仅当$G$有有限指标的紧致阿贝尔子群.然后，我们表明，$A(G)$是弱顺从的，如果组件的身份$G$是阿贝尔，我们证明了一些部分结果走向相反。
On co-amenability for groups and von Neumann algebras
我们首先表明，co-amenability不传递给子群，回答了Eymard在1972年提出的一个问题。然后，我们解决冯诺依曼代数的协变性，特别是描述它是如何与前者。
W*-Amenability for Fell bundles over discrete groups
本文研究了离散群上的$W^*$-Fell bundles的amenability特性，通过近似性质和条件期望进行表征，并证明了amenability在子群限制下的传递性，扩展了经典群amenability的结果。
Amenability for Fell bundles over groupoids
我们建立的条件下，普遍和减少规范一致的费尔丛广群。具体地说，我们证明了可测顺从群胚上任意Fell丛的全代数与约化C* 代数重合，并且证明了对于轨道空间为T_0的群胚G，如果丛对各向同性群的限制的全代数与约化代数重合，则G上Fell丛的全代数与约化代数重合.
Amenability for dual Banach algebras
我们定义一个巴拿赫代数A是对偶的，如果$A = (A_\ast)^\ast$对于$A^\ast$的闭子模$A_\ast$.对偶巴拿赫代数类包括所有的$W^\ast$ -代数，也包括局部紧群G的所有代数M（G），自反Banach空间E的所有代数L（E），以及Arens正则巴拿赫代数的所有双链。一般的印象是，顺从，对偶巴拿赫代数，而不是规则的例外。我们证实了这一印象。我们首先证明了在一定条件下，顺从的对偶巴拿赫代数已经是超顺从的，因此是有限维的。然后，我们开发了两个概念的顺从性-康纳斯顺从性和强康纳斯顺从性-考虑$w^\ast$ -拓扑对偶巴拿赫代数。我们将Arens正则巴拿赫代数A的顺从性与$A^{\ast\ast}$的（强）Connes顺从性联系起来;作为应用，我们证明了存在具有逼近性质的自反Banach空间，使得L（E）不是Connes顺从的。利用伪测度代数刻画了内顺从局部紧群的顺从性。最后，我们证明了顺从von Neumann代数是次齐次代数，从而避免了$C^\ast$ -代数的顺从性与核性的等价性.
Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey
设G是一个局部紧群，A（G）和B（G）表示它的Fourier代数和Fourier-Stieltjes代数.这些代数是群和测度代数L^1（G）和M（G）的对偶对象，在某种意义上推广了阿贝尔群上的庞特里亚金对偶定理。我们希望考虑A（G）和B（G）的顺从性性质，并将它们与L^1（G）和M（G）的此类性质进行比较。对我们来说，“顺从性性质”是指顺从性、弱顺从性和双平坦性，以及一些更适合于特殊设置的性质，如半单交换巴拿赫代数的超Tauberian性质。我们要强调的是，在研究A（G）和B（G）时，算子空间和完全有界映射的理论起着不可缺少的作用。我们还展示了顺从性理论在补理想和同态问题上的一些应用。
The notion of Fréchet locally $C^*$-algebra generalizes the notion of $C^*$-algebra. In this paper, we first present some definitions and basic facts about locally $C^*$-algebra, and then we introduce and study the notion of ideal and weak amenability for these algebras. Also, we show that every Fréchet locally $C^*$-algebra is ideally amenable.
We consider the Fourier-Stietljes algebra B(G) of a locally compact group G. We show that operator amenablility of B(G) implies that a certain semitolpological compactification of G admits only finitely many idempotents. In the case that G is connected, we show that operator amenability of B(G) entails that $G$ is compact.
The operator amenability of uniform algebras
我们证明了M. V. Sheinberg：一个具有规范（即极小）算子空间结构的一致代数是算子顺从的当且仅当它是一个交换$C^\ast$ -代数。
In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally finite extended metric spaces and for general algebras over commutative fields. In the context of algebras we also study the relation of amenability with proper infiniteness. We apply our general analysis to two important classes of algebras: the unital Leavitt path algebras and the translation algebras on locally finite extended metric spaces. In particular, we show that the amenability of a metric space is equivalent to the algebraic amenab…
Connes-amenability and normal, virtual diagonals for measure algebras, I
证明了局部紧群$G$的测度代数$M(G)$是Connes-顺从的当且仅当$G$是顺从的.
Amenability, exactness and weak containment property for groupoids
本文综述群胚$C^*$-代数的精确性概念，并探讨其在弱包含问题中的作用，即完全与约化$C^*$-代数一致是否蕴含群胚顺从性。
In this paper, we introduce actions of fusion algebras on unital $C^*$-algebras, and define amenability for fusion algebraic actions. Motivated by S.\ Neshveyev et al.'s work, considering the co-representation ring of a compact quantum group as a fusion algebra, we define the canonical fusion algebraic (for short, CFA) form of a discrete quantum group action on a compact quantum space. Furthermore, through the CFA form, we define FA-amenability of discrete quantum group actions, and present some basic connections between FA-amenable actions and amenable discrete quantum groups. As an applicati…
Characterization of amenability by a factorization property of the group von Neumann algebra
证明了局部紧群$G$的顺从性等价于由$ VN(G) = <VN(G)^*VN(G)>$给出的$VN(G)$的一个因子分解性质.这部分回答了Z. Hu和M. Neufang等人在他们的文章\textit{Distinguishing properties of Arens irregularity}，Proc.Amer.Math.Soc.137（2009），no.5，1753-1761中描述。
Operator amenability of Fourier-Stieltjes algebras
算子顺从性的概念是由Z. J. Ruan，1995年。他表明，一个局部紧群G是顺从的当且仅当其傅立叶代数A（G）是经营者顺从。本文研究了Fourier-Stieltjes代数B（G）和约化Fourier-Stieltjes代数B_r（G）的算子顺从性。自然的猜想是，这些代数中的任何一个都是算子顺从的当且仅当G是紧的。我们部分地证明了这个猜想与纯粹的运营商顺从性取代运营商C-顺从性，某些常数C < 5。在这个过程中，我们得到了B（G）的一个新的分解，它可以解释为M（G）分解为离散测度和连续测度的非交换对应。我们进一步引入了算子顺从性的一种变体--算子Connes顺从性，它也考虑了B（G）和B_r（G）上的对偶空间结构.证明了B_r（G）是Connes-affected的当且仅当G是affected的.令人惊讶的是，B（F_2）是算子Connes顺从的，尽管两个生成元中的自由群F_2不顺从.
Connes-amenability and normal, virtual diagonals for measure algebras, II
我们证明了对于局部紧群$G$，下列等价：（i）$G$是顺从的;（ii）$M(G)$是Connes-顺从的;（iii）$M(G)$有正规的虚对角线.
A simple proof of a theorem on (2n)-weak amenability
给出了三角巴拿赫代数T= [（AA）（0 A）]的（2n）-弱顺从性的一个简单证明，其中A是有单位元的C* 代数.
Consider an inclusion of diffuse von Neumann algebras A c M . We say that A c M has the absorbing amenability property if for any diffuse subalgebra B c A and any amenable intermediate algebra B c D c M we have that D is contained in A. We prove that the cup subalgebra associated to any subfactor planar algebra has the absorbing amenability property.
Generalized amenability in quantum groups
本文研究局部紧量子群的广义可amenability，证明在协方差和可迹性条件下，由量子左正则表示生成的C*-代数的近似可amenability蕴含量子群具有不变量子平均，并推广到前对偶代数情形。
Singly generated operator algebras satisfying weakened versions of amenability
我们构造了${\mathcal K}({\mathcal H})$的一个单生成子代数，它是不可修改的，但却是有界近似可收缩的。这个例子嵌入到齐次冯诺依曼代数中。我们还观察到有限型I冯诺依曼代数中存在单生成的双平坦子代数，它们不顺从（因此不同构于C* 代数）。这样一个例子可以用来表明，交换算子代数的某种扩张性质（在arXiv：1012.4259中表示为顺从性）并不一定意味着顺从性。
Amenability for unitary groups of C*-algebras
本文提出刻画幺正C*-代数酉群顺从性的猜想，证明了其对特定类C*-代数成立，并基于Kirchberg工作给出Ng相关问题的反例。
Operator amenability of Fourier-Stieltjes algebras, II
我们给出了一个非紧的局部紧群$G$的例子，使得它的Fourier-Stieltjes代数$B(G)$是算子顺从的.此外，我们描述了那些$G$，$A^*(G)$ -脊柱的$B(G)$介绍M。Ilie和第二个命名的作者-是经营者服从，并表明，$A^*(G)$是经营者弱服从每个$G$。
We prove the existence of a linear isometric correspondence between the Banach space of all symmetric orthogonal forms on a JB$^*$-algebra $\mathcal{J}$ and the Banach space of all purely Jordan generalized derivations from $\mathcal{J}$ into $\mathcal{J}^*$. We also establish the existence of a similar linear isometric correspondence between the Banach spaces of all anti-symmetric orthogonal forms on $\mathcal{J}$, and of all Lie Jordan derivations from $\mathcal{J}$ into $\mathcal{J}^*$.
In this work we introduce and study a new notion of amenability for actions of locally compact groups on $C^*$-algebras. Our definition extends the definition of amenability for actions of discrete groups due to Claire Anantharaman-Delaroche. We show that our definition has several characterizations and permanence properties analogous to those known in the discrete case. For example, for actions on commutative $C^*$-algebras, we show that our notion of amenability is equivalent to measurewise amenability. Combined with a recent result of Alex Bearden and Jason Crann, this also settles a long s…
In this paper we prove that the Thompson groups $T$ and $V$ are not inner amenable. In particular, their group von Neumann algebras do not have property $Γ$. Moreover, we prove that if the reduced group $C^\ast$-algebra of $T$ is simple, then the Thompson group $F$ is non-amenable. Furthermore, we give a few new equivalent characterizations of amenability of $F$.
Amenability of group actions on compact spaces and the associated Banach algebras
本文将拓扑群顺从性的经典刻画推广至紧 Hausdorff 空间上的离散群作用，通过引入自然关联的 Banach 代数和弱化的顺从性概念，获得了顺从作用的类似刻画，并证明了加强 Dong 和 Wang (2015) 定理的不动点性质。
Amenability for unitary groups of simple monotracial C*-algebras
本文证明单位正则无限核C*-代数的等距半群右可 Amenability，且迹 GNS 表示超有限的单位单迹C*-代数的酉群在弱拓扑下斜可 Amenability，部分解决相关猜想与问题。
Factorization and weak amenability of A(X)
研究了巴拿赫空间X上可逼近算子的巴拿赫代数A（X）的弱顺从性及其与A（X）中算子因子分解性质的关系.我们表明，如果A（X）是弱顺从的，那么要么A（X）是自诱导（一个很好的因式分解性质），或X是非常特殊的，结合了一些奇异的性质的空间的Gowers和Maurey和Pisier。在自诱导巴拿赫代数类中，我们证明了弱顺从性在Morita型等价下是保持的。利用这一点，我们推广了A. Blanco关于A（X）的弱顺从性.
Group amenability properties for von Neumann algebras
在他对顺从的酉表示的研究中，M. E. B.贝卡问是否有一个类似的代表性显着的定点财产顺从的群体。在本文中，我们证明了这样一个不动点定理在更一般的背景下的$G$ -顺从冯诺依曼代数$M$，其中$G$是一个局部紧群作用在$M$。本文将Connes和Bekka的Følner条件推广到$M$是半有限的，并且有一个忠实的、半有限的、正规的迹在$G$作用下不变的情形.
Using ultrapowers of $C^{\ast}$-algebras we provide a new construction of the multiplier algebra of a $C^{\ast}$-algebra. This extends the work of Avsec and Goldbring [Houston J. Math., to appear, arXiv:1610.09276.] to the setting of noncommutative and nonseparable $C^{\ast}$-algebras. We also extend their work to give a new proof of the fact that groups that act transitively on locally finite trees with boundary amenable stabilizers are boundary amenable.
This paper concerns the study of regular Fourier hypergroups through multipliers of their associated Fourier algebras. We establish hypergroup analogues of well-known characterizations of group amenability, introduce a notion of weak amenability for hypergroups, and show that every discrete commutative hypergroup is weakly amenable with constant 1. Using similar techniques, we provide a sufficient condition for amenability of hypergroup Fourier algebras, which, as an immediate application, answers one direction of a conjecture of Azimifard--Samei--Spronk [J. Funct. Anal. 256(5) 1544-1564, 2009…
Symmetrized pseudofunction algebras from $L^p$-representations and amenability of locally compact groups
本文运用复插值理论将局部紧群的$L^p$-伪函数代数定位在$L^1(G)$与$C^*(G)$之间，推广了Herz的群顺从性刻画至对称化设置，并描述了其Banach空间对偶。
We show that for a connected Lie group $G$, its Fourier algebra $A(G)$ is weakly amenable only if $G$ is abelian. Our main new idea is to show that weak amenability of $A(G)$ implies that the anti-diagonal, $\checkΔ_G=\{(g,g^{-1}):g\in G\}$, is a set of local synthesis for $A(G\times G)$. We then show that this cannot happen if $G$ is non-abelian. We conclude for a locally compact group $G$, that $A(G)$ can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group $G$, $A(G)$ is weakly amenable if and only if its connected component of…
Building on our previous work, we study the non-relative homology of quantum group convolution algebras. Our main result establishes the equivalence of amenability of a locally compact quantum group $\mathbb{G}$ and 1-injectivity of $L^{\infty}(\widehat{\mathbb{G}})$ as an operator $L^1(\widehat{\mathbb{G}})$-module. In particular, a locally compact group $G$ is amenable if and only if its group von Neumann algebra $VN(G)$ is 1-injective as an operator module over the Fourier algebra $A(G)$. As an application, we provide a decomposability result for completely bounded $L^1(\widehat{\mathbb{G}}…
On weak amenability of Fourier algebras
本文将连通 Lie 群 Fourier 代数弱顺从当且仅当群交换的结论，推广至一般连通局部紧群，扩展了 Choi 和 Ghandehari 的特殊情形方法。
$(σ,τ)$-amenability of $C^*$-algebras
设${\mathcal A}$是一个代数，$σ,τ:{\mathcal A}\to{\mathcal A}$是两个线性映射，使得$σ({\mathcal A})$和$τ({\mathcal A})$都是${\mathcal A}$的子代数，${\mathcal X}$是一个$\big(τ({\mathcal A}),σ({\mathcal A})\big)$ -双模.如果$D(ab)=D(a)\cdotσ(b)+τ(a)\cdot D(b) (a,b\in {\mathcal A})$是线性映射，则称$D:{\mathcal A}\to {\mathcal X}$为$(σ,τ)$ -导子.如果存在$x\in{\mathcal X}$使得$D$的形式为$D_x^-(a)=x\cdot σ(a)-τ(a)\cdot x (a\in {\mathcal A})$或$D_x^ +(a)=x\cdot σ(a)+τ(a)\cdot x (a\in {\mathcal A})$，则$(σ,τ)$ -派生$D$称为$(σ,τ)$ -内部派生.一个Banach代数${\mathcal A}$称为$(σ,τ)$ -顺从的，如果从${\mathcal A}$到一个对偶Banach $\big(τ({\mathcal A}),σ({\mathcal A})\big)$ -双模的每个$(σ,τ)$ -导子…
Twisted Fourier(-Stieltjes) spaces and amenability
本文通过群上的2-上闭链引入Fourier(-Stieltjes)代数的推广，研究相关乘子空间性质，并证明通过比较扭曲Fourier-Stieltjes空间与乘子空间刻画局部紧群顺从性的结论。
Operator amenability of the Fourier algebra in the cb-multiplier norm
设$G$是局部紧群，$A_\cb(G)$表示$G$的傅里叶代数$A(G)$在$A(G)$的完全有界乘子空间中的闭包.如果$G$是一个弱顺从的离散群，使得$\cstar(G)$是剩余有限维的，我们证明了$A_\cb(G)$是算子顺从的。特别是，$A_\cb(F_2)$是操作者顺从的，即使$F_2$，两个生成器中的自由群不是顺从群。此外，我们还证明了，如果$G$是一个离散群，使得$A_\cb(G)$是算子顺从的，则$A(G)$的闭理想在$A(G)$中弱完全可补当且仅当它有一个在cb-乘子范数中有界的近似恒等式.
Amenability for groups can be extended to metric spaces, algebras over commutative fields and $C^*$-algebras by adapting the notion of Følner nets. In the present article we investigate the close ties among these extensions and show that these three pictures unify in the context of the uniform Roe algebra $C_u^*(X)$ over a metric space $(X,d)$ with bounded geometry. In particular, we show that the following conditions are equivalent: (1) $(X,d)$ is amenable; (2) the translation algebra generating $C_u^*(X)$ is algebraically amenable (3) $C_u^*(X)$ has a tracial state; (4) $C_u^*(X)$ is not pro…
Amenability for Fell Bundles
给定一个离散群$Γ$上的Fell丛$\B$，我们构造了它的约化截面代数$C^*_r(\B)$，类似于C*-动力系统的约化交叉积.当$\B$的约化截面代数与全截面代数同构时，我们称丛是顺从的。然后，我们制定了一个近似属性，我们证明是一个充分条件顺从。本文研究了具有条件期望的$Γ$ -分次C*-代数，并讨论了与分次有关的Fell丛.我们表明，例如，所有这样的代数是同构的$C^*_r(\B)$，当丛是顺从的。我们还研究了分次C*-代数中的诱导理想，得到了Stratila和Voiculescu关于AF-代数和Nica关于拟格序群的结果的推广。简要评论的相关性，我们的理论，一定的开放问题的理论中的精确C*-代数。给出了Quigg和Raeburn最近发现的Cuntz-Krieger代数$O_A$的$F_n$ -分次的一个应用.具体地说，我们证明了Cuntz Krieger丛满足近似性质，因此是顺从的，对于所有矩阵$A$的条目在{0，1}，即使$A$不满足众所周知的性质（I）研究的Cuntz和Krieger在他们的论文。
We analyze the dichotomy amenable/paradoxical in the context of (discrete, countable, unital) semigroups and corresponding semigroup rings. We consider also Følner's type characterizations of amenability and give an example of a semigroup whose semigroup ring is algebraically amenable but has no Følner sequence. In the context of inverse semigroups $S$ we give a characterization of invariant measures on $S$ (in the sense of Day) in terms of two notions: $domain$ $measurability$ and $localization$. Given a unital representation of $S$ in terms of partial bijections on some set $X$ we define a n…
Group von Neumann algebras, inner amenability, and unit groups of continuous rings
本文证明非内顺从离散群 $G$ 的群冯诺依曼代数相伴算子环的单位群在 rank 度量拓扑下非顺从，由此构造出非顺从单位群的非离散不可约连续环实例，并建立与 $\mathrm{II}_{1}$ 因子酉群 Eymard--Greenleaf 顺从性的联系。
On amenability constants of Fourier algebras: new bounds and new examples
本文通过非交换傅里叶分析，为离散群的傅里叶代数可 amenability 常数提供了更精确的上界，并展示了新的离散和紧致群例子，支持了Runde的下界猜想。
Vanishing of the first $(σ,τ)$-cohomology group of triangular Banach algebras
本文定义了第一拓扑$(σ,τ)$ -上同调群，并研究了某些三角巴拿赫代数的第一$(σ,τ)$ -上同调群的消失.我们应用这些结果研究了三角巴拿赫代数的$(σ,τ)$ -弱顺从性和$(σ,τ)$ -顺从性.
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