Related papers: $p$-Fourier algebras on compact groups

In this paper, some known results will be generalized. Firstly, the idempotent theorem on the Fourier-Stieltjes algebra will be promoted and linked to the $p$-analog of such an algebra. Next, the $p$-analog of the $\pi$-Fourier space…

The Fourier and Fourier-Stieltjes algebras $A(G)$ and $B(G)$ of a locally compact group $G$ are introduced and studied in 60's by Piere Eymard in his PhD thesis. If $G$ is a locally compact abelian group, then $A(G)\simeq L^1(\hat{G})$, and…

Let WAP(A) be the space of all weakly almost periodic functionals on a Banach algebra A. The Banach algebra A for which the natural embedding of A into WAP(A)* is bounded below is called a WAP-algebra. We show that the second dual of a…

We give a description of operator algebras of free wreath products in terms of fundamental algebras of graphs of operator algebras as well as an explicit formula for the Haar state. This allows us to deduce stability properties for certain…

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…

For $G$ a connected, reductive group over an algebraically closed field $k$ of large characteristic, we use the canonical Springer isomorphism between the nilpotent variety of $\mathfrak{g}:=\mathrm{Lie}(G)$ and the unipotent variety of $G$…

In this paper we study the ideal amenability of Banach algebras. Let $\cal A$ be a Banach algebra and let $I$ be a closed two-sided ideal in $\cal A$, $\cal A$ is $I$-weakly amenable if $H^{1}({\cal A},I^*)=\{0\}$. Further, $\cal A$ is…

Let $G$ a locally compact abelian group with Haar measure $\mu$ and let $1<p<\infty. $ In the present paper we determine necessary and sufficient conditions on $G$ for the grand Lebesgue space $ L^{p),\theta}(G)$ to be a Banach algebra…

Let I be a symmetrically-normed ideal of the space of bounded operators acting on a Hilbert space H. Let ${p_i}_1 ^w$ $(1\leq w \leq \infty)$ be a family of mutually orthogonal projections on H. The pinching operator associated with the…

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 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 introduce and study various notions of amenability continuous (Borel) partial actions of locally compact (Borel) groups $G$ on topological (standard Borel) spaces. We also study amenability of partial representations of a locally compact…

We study amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and apply it to algebras associated with finitely generated groups. We show that a group G is amenable if and only if its group…

A locally compact group $G$ has property PL if every isometric $G$-action either has bounded orbits or is (metrically) proper. For $p>1$, say that $G$ has property $BP_{L^p}$ if the same alternative holds for the smaller class of affine…

We prove that the Fourier space of a hypergroup constructed from a conditional expectation on a locally compact group has a Banach algebra structure.

Let $T:Y\to X$ be a bounded linear operator between two normed spaces. We characterize compactness of $T$ in terms of differentiability of the Lipschitz functions defined on $X$ with values in another normed space $Z$. Furthermore, using a…

Let $G$ be a locally compact group, $A_p (G)$ be the Herz algebra of $G$ associated with $1 <p< \infty$. We show that $A_p (G)$ is Arens regular if and only if $G$ is a discrete group and for each countable subgroup $H$ of $G$, $A_p (H)$ is…

Let G be an exceptional Lie group with a maximal torus T. Based on common properties in the Schubert presentation of the cohomology ring H*(G/T;F_{p}) DZ1, and concrete expressions of generalized Weyl invariants for G over F_{p}, we obtain…

We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the…

For a locally convex $^*$-algebra $A$ equipped with a fixed continuous $^*$-character $\varepsilon$, we define a cohomological property, called property $(FH)$, which is similar to character amenability. Let $C_c(G)$ be the space of…