Related papers: On the algebraic structures in $\A_\Phi(G)$

In this paper, we characterize the amenablity of locally compact groups in terms of the properties of the Orlicz Figa-Talamanca Herz algebras.

Let $G$ be a locally compact group. We show that its Fourier algebra $A(G)$ is amenable if and only if $G$ has an abelian subgroup of finite index, and that its Fourier-Stieltjes algebra $B(G)$ is amenable if and only if $G$ has a compact,…

Let $G$ be a locally compact abelian group, and let $\omega:G \to [1,\infty)$ be a measurable weight, i.e., $\omega$ is measurable, and $\omega(s+t)\leq \omega(s)\omega(t)$ for all $s, t \in G$. Let $\mathcal{A}$ be a semisimple commutative…

In this paper, we introduce a homological notion of left $\phi$-biprojectivity for Banach algebras, where $\phi$ is a non-zero multiplicative linear functional. We show that for a locally compact group $G$, the Segal algebra $S(G)$ is left…

In this article, we introduce and explore the notion of topological amenability in the broad setting of (locally compact) semihypergroups. We acquire several stationary, ergodic and Banach algebraic characterizations of the same in terms of…

Let $G$ be a locally compact group, and let $WAP(G)$ denote the space of weakly almost periodic functions on $G$. We show that, if $G$ is a $[SIN]$-group, but not compact, then the dual Banach algebra $WAP(G)^\ast$ does not have a normal,…

We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity.…

Let $G$ be a semiabelian variety defined over an algebraically closed field $K$, endowed with a rational self-map $\Phi$. Let $\alpha\in G(K)$ and let $\Gamma\subseteq G(K)$ be a finitely generated subgroup. We show that the set…

We show via an application of techniques from complex interpolation theory how the $L^p$-pseudofunction algebras of a locally compact group $G$ can be understood as sitting between $L^1(G)$ and $C^*(G)$. Motivated by this, we collect and…

In this paper, we study the notion of approximately bi at Banach algebras for second dual Banach algebras and semigroup algebras. We show that for a locally compact group G, if S(G)?? is approximately bi at, then G is amenable group. Also…

Let G be a locally compact group, and let A(G) and B(G) denote its Fourier and Fourier-Stieltjes algebras. These algebras are dual objects of the group and measure algebras, L^1(G) and M(G), in a sense which generalizes the Pontryagin…

It is shown that for a locally compact group $G$, if $L^{1}(G)^{**}$ is approximately weakly amenable, then $M(G)$ is approximately weakly amenable. Then, new notions of approximate weak amenability and approximate cyclic amenability for…

We examine the analyticity of the class of separable Banach spaces possessing the $\pi$-property, defined in terms of convergence along a filter. Our results establish that this class is $\Sigma^1_3$ whenever the underlying filter is…

An Orlicz space $L^{\Phi}(\Omega)$ is a Banach function space defined by using a Young function $\Phi$, which generalizes the $L^p$ spaces. We show that, for a reflexive Orlicz space $L^{\Phi}([0,1])$, a locally compact second countable…

Let $A_p(G)$ denote the Figa-Talamanca-Herz Banach Algebra of the locally compact group $G$, thus $A_2(G)$ is the Fourier Algebra of $G$. If $G$ is commutative then $A_2(G)=L^1(\hat{G}){\hat{}}$. Let $A^r_p(G)=A_p\cap L^r(G)$ with norm…

Let $G$ be a compact group, let $X$ be a Banach space, and let $P\colon L^1(G)\to X$ be an orthogonally additive, continuous $n$-homogeneous polynomial. Then we show that there exists a unique continuous linear map $\Phi\colon L^1(G)\to X$…

For a locally compact group $G$, let $A(G)$ denote its Fourier algebra and $\hat{G}$ its dual object, i.e. the collection of equivalence classes of unitary represenations of $G$. We show that the amenability constant of $A(G)$ is less than…

Let $G$ be a locally elliptic group, $(\Phi,\Psi)$ a complementary pair of Young functions, and $\omega: G \rightarrow [1,\infty)$ a weight function on $G$ such that the weighted Orlicz space $L^\Phi(G,\omega)$ is a Banach $*$-algebra when…

Let $\frak{F}(X, A)$ be one of the Banach algebras $\hbox{Lip}(X, A)$ or $\hbox{lip}(X, A)$. In this paper, we show that $\frak{F}(X, A)$ is amenable if and only if $X$ is uniformly discrete and $A$ is amenable. We also prove that the…

We define and study the notion of property $(\rm T)$ for Banach algebras, generalizing the one from $C^*$-algebras. For a second countable locally compact group $G$ and a given family of Banach spaces $\mathcal E$, we prove that our Banach…