A. Yu. Pirkovskii
For a locally compact group G, the convolution product on the space N(L^p(G)) of nuclear operators was defined by Neufang. We study homological properties of the convolution algebra N(L^p(G)) and relate them with some properties of the group G, such as compactness, finiteness, discreteness, and amenability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We show that the biflatness - in the sense of A. Ya. Helemskii - of the Fourier algebra $A(G)$ of a locally compact group $G$ forces $G$ to either have an abelian subgroup of finite index or to be non-amenable without containing $F_2$, the free group in two generators, as a closed subgroup. An analogous dichotomy is obtained for biprojectivity.
In this paper, we study left $ϕ$-biflatness and left $ϕ$-biprojectivity of some Banach algebras, where $ϕ$ is a non-zero multiplicative linear function. We show that if the Banach algebra $A^{**}$ is left $ϕ$-biprojective, then $A$ is left $ϕ$-biflat. Using this tool we study left $ϕ$-biflatness of some matrix algebras. We also study left $ϕ$-biflatness and left $ϕ$-biprojectivity of the projective tensor product of some Banach algebras. We prove that for a locally compact group $G$, $M(G)\otimes_{p} A(G)$ is left $ϕ\otimes ψ$-biprojective if and only if $G$ is finite. We show that $M(G)\otime…
In this paper we are going to investigate the approximate biprojectivity and the $ϕ$-biflatness of some Banach algebras related to the locally compact groups. We show that a Segal algebra $S(G)$ is approximate biprojective if and only if $G$ is compact. Also for a continuous weight $w\geq 1$, we show that $L^{1}(G,w)$ is a approximate biprojective if and only if $G$ is compact. We study $ϕ$-biflatness of some Banach algebras, where $ϕ:A\rightarrow \mathbb{C}$ is a multiplicative linear functional. We show that if $S(G)$ is $ϕ$-biflat, then $G$ is amenable group. Also we show that the $ϕ$-bifla…
Given a Banach algebra $ \mathcal{A} $ and a continuous homomorphism $σ$ on it, the notion of $σ$-biflatness for $ \mathcal{A} $ is introduced. This is a generalization of biflatness and it is shown that they are distinct. The relations between $σ$-biflatness and some other close concepts such as $σ$-biprojectivity and $σ$-amenability are studied. The $σ$-biflatness of tensor product of Banach algebras are also discussed.
In this paper, we study the notion of $ϕ$-biflatness, $ϕ$-biprojectivity, approximate biprojectivity and Johnson pseudo-contractibility for a new class of Banach algebras. Using this class of Banach algebras we give some examples which are approximately biprojective. Also some Banach algebras are given among matrix algebras which are never Johnson pseudo-contractible.
We give a survey of our recent results on homological properties of K"othe algebras, with an emphasis on biprojectivity, biflatness, and homological dimension. Some new results on the approximate contractibility of K"othe algebras are also presented.
In this paper we define module biprojctivity and module biflatness for a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and find their relation to classical biprojectivity and biflatness. As a typical example, We show that for an inverse semigroup $S$ with an upward directed set of idempotents $E$, the semigroup algebra $ \ell ^{1}(S)$, as an $\ell ^{1}(E)$-module, is module biprojective if and only if an appropriate group homomorphic image of $S$ is finite. Also we show that $\ell ^{1}(S)$ is module biflat if and only if $S$ is amenable.
Let T be a homomorphism from a Banach algebra B to a Banach algebra A.The Cartesian product space A * B with T-Lau multiplication and l^1-norm becomes a new Banach algebra A *_T B. We investigate the notions such as approximate amenability, pseudo amenability, phi-pseudo amenability,phi-biflatness and phi-biprojectivity for Banach algebra A *_T B. We also present an example to show that approximate amenability of A and B is not stable for A *_T B. Finally we characterize the double centralizer algebra of A *_T B and present an application of this characterization.
In this paper, we introduce a new notion of biprojectivity, called $WAP$-biprojectivity for $F(\mathcal{A})$, the enveloping dual Banach algebra associated to a Banach algebra $\mathcal{A}$. We find some relations between Connes biprojectivity, Connes amenability and this new notion. We show that, for a given dual Banach algebra $\mathcal{A}$, if $F(\mathcal{A})$ is Connes amenable, then $\mathcal{A}$ is Connes amenable. For an infinite commutative compact group $G$, we show that the convolution Banach algebra $F(L^2(G))$ is not $WAP$-biprojective. Finally, we provide some examples of the enve…
In this paper, we investigate homological properties of Banach algebras. We show that retractions Banach algebras preserve biprojectivity, contractibility and biflatness. We also prove that contractibility of second dual of a Banach algebra implies contractibility of the Banach algebra. For a Banach algebra $A$ with $Δ(A)\neq\emptyset$, let $\frak{F}(X, A)$ be one of the Banach algebras $C_b(X, A)$, $C_0(X, A)$, $\hbox{Lip}_α(X, A)$ or $\hbox{lip}_α(X, A)$. In the following, we study homological properties of Banach algebra $\frak{F}(X, A)$, especially contractibility of it. We prove that cont…
In this paper, we introduce a notion of approximate Connes-biprojectivity for dual Banach algebras. We study the relation between approximate Connes-biprojectivity, Johnson pseudo-Connes amenability and $φ$-Connes amenability. We propose a criterion to show that some certain dual triangular Banach algebras are not approximately Connes-biprojective. Next we show that for a locally compact group $G$, the Banach algebra $M(G)$ is approximately Connes-biprojective if and only if $G$ is amenable. Finally for an infinite commutative compact group $G$ we show that the Banach algebra $L^2(G)$ with con…
Building on an old result of Duncan and Namioka, we show that the ${\ell}^1$-convolution algebra of a semilattice $S$ is biflat precisely when $S$ is uniformly locally finite. The proof shows in passing that for such $S$ the convolution algebra is isomorphic to ${\ell}^1(S)$ with pointwise multiplication. At the end we sketch how these techniques may be extended to prove an analogous characterisation of biflatness for Clifford semigroup algebras.
Given a (reduced) locally compact quantum group $A$, we can consider the convolution algebra $L^1(A)$ (which can be identified as the predual of the von Neumann algebra form of $A$). It is conjectured that $L^1(A)$ is operator biprojective if and only if $A$ is compact. The "only if" part always holds, and the "if" part holds for Kac algebras. We show that if the splitting morphism associated with $L^1(A)$ being biprojective can be chosen to be completely positive, or just contractive, then we already have a Kac algebra. We give another proof of the converse, indicating how modular properties …
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。