A simple proof of a theorem on (2n)-weak amenability
M. S. Moslehian, F. Negahban
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.
A simple proof of (2n)-weak amenability of the triangular Banach algebra T= [(A A) (0 A)] is given where A is a unital C*-algebra.
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A new proof of extreme amenability of the unitary group of the hyperfinite II$_1$-factor
给出了具有强算子拓扑的超有限II ${}_1$ -因子von Neumann代数的酉群的极端顺从性的另一种证明.
Using the recently developed notion of a Herz--Schur multiplier of a C*-dynamical system we introduce weak amenability of C*- and W*-dynamical systems. As a special case we recover Haagerup's characterisation of weak amenability of a discrete group. We also consider a generalisation of the Fourier algebra to crossed products and study its multipliers.
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。
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.
$C^*$-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.
A note on weak amenability for reduced free products of discrete quantum groups
证明了Cowling-Haagerup常数等于1的弱顺从离散量子群的约化自由积的Cowling-Haagerup常数也等于1。
Amenability and co-amenability in non-abelian group duality
由于引理3.4的证明存在空白，本文已被作者撤回
An invitation to weak amenability, after Cowling and Haagerup
本文面向局部紧群，系统介绍弱可和性概念，并梳理 Cowling 与 Haagerup 以来的关键研究成果。
Weak amenability of Coxeter groups
设（G，S）是Coxeter群.我们构造了与正定函数g -> r^l（g）相关的酉表示到开单位圆盘的延拓。(Here 0<r<1，并且l表示关于生成集S的长度函数。所构造的表示是一致有界的，并证明了这蕴涵着群G的弱顺从性。
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.
Weak amenability and simply connected Lie groups
根据小泽的方法，我们证明了几个半直积是不弱服从。因此，我们能够刻画弱服从的单连通李群。
We completely characterize connected Lie groups all of whose countable subgroups are weakly amenable. We also provide a characterization of connected semisimple Lie groups that are weakly amenable. Finally, we show that a connected Lie group is weakly amenable if the group is weakly amenable as a discrete group.
Proper cocycles and weak forms of amenability
设$G$和$H$是局部紧的第二可数群。假设$G$在标准概率空间$(X,μ)$上以测度类保持方式作用，使得$L^\infty(X,μ)$具有不变平均，并且存在在适当的自然意义上是适当的Borel上循环$α:G\times X\rightarrow H$。证明了若$H$具有Haagerup性质（a-T-可解性）、弱可解性或弱Haagerup性质之一，则$G$也具有上述性质.我们观察到，这是一个弱形式的测量等价对离散群的情况下。
Weak amenability of CAT(0) cubical groups
证明了如果G是一个离散群，且G在有限维CAT（0）立方复形X上有度量恰当作用，则G是弱顺从的。我们通过构造一致有界的希尔伯特空间表示来做到这一点，其中量z^{l（g）}是矩阵系数。这里l是G上的一个长度函数，它是由复形X上的组合距离函数得到的。
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。
We show that, if $G$ is an amenable group and $H$ is a hyperbolic group, then the free product $G\ast H$ is weakly amenable. A key ingredient in the proof is the fact that $G\ast H$ is orbit equivalent to $\mathbb{Z}\ast H$.
Jordan weak amenability and orthogonal forms on JB*-algebras
证明了JB $^*$ -代数$\mathcal{J}$上的所有对称正交型的Banach空间与从$\mathcal{J}$到$\mathcal{J}^*$的所有纯Jordan广义导子的巴拿赫空间之间存在线性等距对应.我们还建立了一个类似的线性等距对应之间的巴拿赫空间的所有反对称正交形式的$\mathcal{J}$，和所有李乔丹导子从$\mathcal{J}$到$\mathcal{J}^*$。
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…
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。
Weak amenability of locally compact quantum groups and approximation properties of extended quantum SU(1,1)
研究了局部紧量子群在Kustermans和Vaes意义下的弱顺从性.特别是，我们专注于非离散的例子。我们证明了一个可合作的量子群是弱可合作的，如果在Fourier代数A（G）中存在一个正的标度不变元网，其表示乘子在C_0（G）中形成一个近似恒等式，该恒等式在M_0A（G）范数下有界，该界是Cowling-Haagerup常数的上估计.作为应用，我们得到了扩展量子SU（1，1）群及其对偶的近似性质。也就是说，我们证明了它是弱顺从和可顺从的。此外，它具有由Daws，Fima，Skalski和White引入的量子群意义下的Haagerup性质。
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。
Weak amenability for subfactors
我们定义了II_1型极值有限指标子因子的弱顺从性和Cowling-Haagerup常数的概念。我们证明了Cowling-Haagerup常数只依赖于子因子的标准不变量。因此，我们定义了标准不变量的Cowling-Haagerup常数。我们明确地计算常数Bisch-Haagerup子因子，并证明它等于常数的建设中所涉及的组。给出有限族Popa意义下的顺从标准不变量，证明了它们的Bisch-Jones意义下的自由积弱顺从常数为1.证明了有限族标准不变量的张量积的Cowling-Haagerup常数等于它们的Cowling-Haagerup常数的乘积.
We use $\mathrm{C}^{\ast}$-algebra ultrapowers to give a new construction of the Stone-Cech compactification of a separable, locally compact space. We use this construction to give a new proof of the fact that groups that act isometrically, properly, and transitively on trees are boundary amenable.
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…
We prove that cocompact (and more generally: undistorted) lattices on $\tilde{A}_2$-buildings satisfy Lafforgue's strong property (T), thus exhibiting the first examples that are not related to algebraic groups over local fields. Our methods also give two further results. First, we show that the first $\ell^p$-cohomology of an $\tilde{A}_2$-building vanishes for any finite $p$. Second, we show that the non-commutative $L^p$-space for $p$ not in $[\frac 4 3,4]$ and the reduced $C^*$-algebra associated to an $\tilde{A}_2$-lattice do not have the operator space approximation property and, consequ…
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。
Examples of groups which are not weakly amenable
证明了局部紧群的弱顺从性对顺从闭正规子群施加了一个强条件。这推广了Haagerup（1988）和Ozawa-Popa（2010）的非弱顺从性结果。一个冯诺依曼代数模拟也得到了。
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。
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$G$。
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}}…
The weak Haagerup property II: Examples
局部紧群的弱Haagerup性质和弱Haagerup常数是第二作者最近引进的。弱Haagerup性质比Cowling和第一作者引入的弱顺从性和Connes和Choda引入的Haagerup性质都弱。本文证明了连通单李群G具有弱Haagerup性质当且仅当G的实秩为0或1。因此，对于连通的单李群，弱Haagerup性质与弱顺从性一致。此外，它证明了，对于连通的单李群的弱Haagerup常数与弱顺从常数一致，虽然这是不正确的局部紧群一般。证明了R^2与SL（2，R）的半直积不具有弱Haagerup性质.
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…
A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for transformation groupoids relative to actions of exact discrete groups. We believe that for general étale groupoids one should have the same equivalence of the two properties under some mild exactness assumption. In this paper we try to support this statement.
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 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。
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.
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。
Given a countable residually finite group, we construct a compact group K and two elements w and u of K with the following properties: The group generated by w and the cube of u is amenable, the group generated by w and u contains a copy of the given group, and these two groups are dense in K. By combining it with a construction of non-exact groups that are LEF by Osajda and Arzhantseva--Osajda and formation of diagonal products, we construct an example for which the latter dense group is non-exact. Our proof employs approximations in the space of marked groups of LEF ("Locally Embeddable into…
Tracially amenable actions and purely infinite crossed products
本文引入迹顺从作用概念并给出等价刻画，证明含自由群F2的群在简单、单位、Z-稳定C*-代数上的外迹顺从作用具有纯无限交叉积，并提供自由群在AF-代数上的具体例子。
Groupoid exactness and the weak containment problem
研究局部紧群体中精确性的类比，证明六个精确性概念的等价性，并探讨群体可接受性与C*-代数关系。
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.
We prove an extension property for $M_d$-multipliers from a subgroup to the ambient group, showing that $M_{d+1}(G)$ is strictly contained in $M_d(G)$ whenever $G$ contains a free subgroup. Another consequence of this result is the stability of the $M_d$-approximation property under group extensions. We also show that Baumslag-Solitar groups are $M_d$-weakly amenable with $\boldsymbolΛ(\operatorname{BS}(m,n),d)=1$ for all $d\geq 2$. Finally, we show that, for simple Lie groups with finite centre, $M_d$-weak amenability is equivalent to weak amenability, and we provide some estimates on the con…
Permanence of approximation properties for discrete quantum groups
证明了离散量子群的弱顺从性持久性和Haagerup性质的几个结果。特别是，我们改进了已知的事实，自由积允许合并在有限量子子群。我们还定义了离散量子群的相对顺从性的概念，并将其与冯诺依曼代数的顺从等价联系起来，给出了额外的持久性性质。
Decomposable Fourier Multipliers and an Operator-Algebraic Characterization of Amenability
本文研究局部紧群上可分解傅里叶乘子代数与傅里叶-斯蒂尔杰斯代数的关系，证明离散群情形等距同构，并利用压缩投影给出顺从性的新算子代数刻画，揭示调和分析、算子代数与群几何的结构联系。
Von Neumann equivalence and $M_d$ type approximation properties
本文研究$M_d$型逼近性质，证明三类性质在von Neumann等价（含测度等价与W*-等价）下稳定，并可由格继承。
Approximation properties of simple Lie groups made discrete
本文考虑一类具有离散拓扑的连通单李群。我们证明了在这类群中下列逼近性质是等价的：（1）Haagerup性质;（2）弱顺从性;（3）弱Haagerup性质。为了得到上述结果，我们证明了离散群GL（2，K）对任意域K弱服从常数1。
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