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

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,…

Let $G$ be a locally compact second countable groupoid with a fixed Haar system $\lambda=\{\lambda^{u}\}_{u\in G^{0}}$ and $(\Phi,\Psi)$ be a complementary pair of $N$-functions satisfying $\Delta_{2}$-condition. In this article, we…

Let $\omega $ be a weight function on a locally compact group G mand let $ M_* (G, \omega ) $ be the subspace of $ M(G , \omega )^* $ consisting of all functionals that vanish at infinity. In this paper, we first investigate the Arens…

In 1972, B. E. Johnson proved that a locally compact group $G$ is amenable if and only if certain Hochschild cohomology groups of its convolution algebra $L^1(G)$ vanish. Similarly, $G$ is compact if and only if $L^1(G)$ is biprojective: In…

We establish a close link between the amenability of a unitary representation $\pi$ of a group $G$ (in the sense of Bekka) and the concentration property (in the sense of V. Milman) of the corresponding dynamical system $(\s_\pi,G)$, where…

Let $\Ps(\N)$ be the set of all finite subsets of $\N$, endowed with the product topology. A description of the compact subsets of $\Ps(\N)$ is given. Two applications of this result to Banach space theory are shown : (1) a characterization…

In this paper, we study left $\phi$-biflatness and left $\phi$-biprojectivity of some Banach algebras, where $\phi$ is a non-zero multiplicative linear function. We show that if the Banach algebra $A^{**}$ is left $\phi$-biprojective, then…

Let $G$ be a locally compact group and $p,q\in \mathbb{R}$ with $p>1$ $p\not=2$ and $q$ between $2$ and $p$ (if $p<2$ then $p<q<2$, if $p>2$ then $2<q<p.$) The main result of the paper is that $A_q(G)$ multiplies $A_p(G)$, more precisely we…

Let $\mathcal{G}$ be a locally compact $\sigma$-compact Hausdorff ample groupoid on a compact space. In this paper, we further examine the (ubiquitous) fiberwise amenability introduced by the author and Jianchao Wu for $\mathcal{G}$. We…

In this article we observe that a locally compact group $G$ is completely determined by the algebraic properties of its Feichtinger's Segal algebra $S_0(G).$ Let $G$ and $H$ be locally compact groups. Then any linear (not necessarily…

We prove a commutative Gelfand--Naimark type theorem, by showing that the set $C_s(X)$ of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space $X$ (provided with the supremum…

Let $X$ be a compact Hausdorff space and $A$ a Banach algebra. We investigate amenability properties of the algebra $C(X,A)$ of all $A$-valued continuous functions. We show that $C(X,A)$ has a bounded approximate diagonal if and only if $A$…

We show that if $G$ is an amenable group and $A\subseteq G$ has positive upper Banach density, then there is an identity neighborhood $B$ in the Bohr topology on $G$ that is almost contained in $AA^{-1}$ in the sense that $B\backslash…

Let $A$ and $B$ be Banach algebras with bounded approximate identities and let $\Phi:A\to B$ be a surjective continuous linear map which preserves two-sided zero products (i.e., $\Phi(a)\Phi(b)=\Phi(b)\Phi(a)=0$ whenever $ab=ba=0$). We show…

An isometric compact group action $G \times (M,g) \rightarrow (M,g)$ is called polar if there exists a closed embedded submanifold $\Sigma \subseteq M$ which meets all orbits orthogonally. Let $\Pi$ be the associated generalized Weyl group.…

The aim of this paper is to present some results about the space L^\Phi(\nu), where \nu is a vector measure on a compact (not necessarily abelian) group and \Phi is a Young function. We show that under certain conditions, the space…

Let $G$ be a locally compact group which is $\sigma $-compact, endowed with a left Haar measure $\lambda .$ Denote by $e$ the unit element of $G$, and by $B$ an open relatively compact and symmetric neighbourhood of $e$. For every $(p,q) $…

For a compact group $\mathbb{G}$, the functor from unital Banach algebras with contractive morphisms to metric spaces with 1-Lipschitz maps sending a Banach algebra $A$ to the space of $\mathbb{G}$-representations in $A$ preserves filtered…

Let $G$ be a compact group. For $1\leq p\leq\infty$ we introduce a class of Banach function algebras $\mathrm{A}^p(G)$ on $G$ which are the Fourier algebras in the case $p=1$, and for $p=2$ are certain algebras discovered in…

We generalise the definition of a group algebra so that it makes sense for non-locally compact topological groups, in particular, we require that the representation theory of the group algebra is isomorphic (in the sense of Gelfand-Raikov)…