Related papers: Operator space structure and amenability for Fig\`…

Let G be a locally compact group. We use the canonical operator space structure on the spaces $L^p(G)$ for $p \in [1,\infty]$ introduced by G. Pisier to define operator space analogues $OA_p(G)$ of the classical Figa-Talamanca-Herz algebras…

We study a generalisation of operator spaces modelled on $L_p$ spaces, instead of Hilbert spaces, using the notion of $p$-complete boundedness, as studied by Pisier and Le Merdy. We show that the Fig\'a-Talamanca-Herz Algebras $A_p(G)$…

The notions of column and row operator space were extended by A. Lambert from Hilbert spaces to general Banach spaces. In this paper, we use column and row spaces over quotients of subspaces of general $L_p$-spaces to equip several Banach…

We consider the minimal boundedly-translation-invariant Segal algebra $S_0^p(G)$ in the Fig\`{a}-Talamanca--Herz algebra $A_p(G)$ of a locally compact group $G$. In the case that $p=2$ and $G$ is abelian this is the classical Segal algebra…

Let $G$ be a locally compact group, and let ${\cal R}(G)$ denote the ring of subsets of $G$ generated by the left cosets of open subsets of $G$. The Cohen--Host idempotent theorem asserts that a set lies in ${\cal R}(G)$ if and only if its…

For a locally compact group $G$ and $p \in (1,\infty)$, we define and study the Beurling-Figa-Talamanca-Herz algebras $A_p(G,\omega)$. For $p=2$ and abelian $G$, these are precisely the Beurling algebras on the dual group $\hat{G}$. For $p…

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…

The notion of operator amenability was introduced by Z.-J. Ruan in 1995. He showed that a locally compact group G is amenable if and only if its Fourier algebra A(G) is operator amenable. In this paper, we investigate the operator…

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…

We show that, given a Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded)…

It is shown that a locally compact group $G$ is amenable if and only if some certain closed ideals of the Fig\`{a}-Talamanca-Herz algebra $A_{p}(G)$ admit bounded $\Delta$-weak approximate identities. Also, similar results are obtained for…

The paper deals with continuous homomorphisms $S \ni s \mapsto T_s \in L(E)$ of amenable semigroups $S$ into the algebra $L(E)$ of all bounded linear operators on a Banach space $E$. For a closed linear subspace $F$ of $E$, sufficient…

For $p\in [1,\infty)$ we study representations of a locally compact group $G$ on $L^p$-spaces and $QSL^p$-spaces. The universal completions $F^p(G)$ and $F^p_{\mathrm{QS}}(G)$ of $L^1(G)$ with respect to these classes of representations…

There has been a long-standing conjecture in Banach algebra that every amenable operator is similar to a normal operator. In this paper, we study the structure of amenable operators on Hilbert spaces. At first, we show that the conjecture…

Let $G$ be a locally compact group, and let $A_\cb(G)$ denote the closure of $A(G)$, the Fourier algebra of $G$, in the space of completely bounded multipliers of $A(G)$. If $G$ is a weakly amenable, discrete group such that $\cstar(G)$ is…

We introduce a uniform structure on any Hilbert $C^*$-module $\mathcal N$ and prove the following theorem: suppose, $F:{\mathcal M}\to {\mathcal N}$ is a bounded adjointable morphism of Hilbert $C^*$-modules over $\mathcal A$ and $\mathcal…

We prove a quantized version of a theorem by M. V. Sheinberg: A uniform algebra equipped with its canonical, i.e. minimal, operator space structure is operator amenable if and only if it is a commutative $C^\ast$-algebra.

In 1969 Lindenstrauss and Rosenthal showed that if a Banach space is isomorphic to a complemented subspace of an L_p-space, then it is either a script L_p-space or isomorphic to a Hilbert space. This is the motivation of this paper where we…

Extending M.\ Daws' definition of ultra-amenable Banach algebras, we introduce the notion of operator ultra-amenability for completely contractive Banach algebras. For a locally compact group $G$, we show that the operator ultra-amenability…

For a locally compact group $G$ and $p \in (1,\infty)$, we define $B_p(G)$ to be the space of all coefficient functions of isometric representations of $G$ on quotients of subspaces of $L_p$ spaces. For $p =2$, this is the usual…