Related papers: Representations of $p$-convolution algebras on $L^…

For $p,q\in [1,\infty)$, we study the isomorphism problem for the $p$- and $q$-convolution algebras associated to locally compact groups. While it is well known that not every group can be recovered from its group von Neumann algebra, we…

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…

We continue our study of group algebras acting on $L^p$-spaces, particularly of algebras of $p$-pseudofunctions of locally compact groups. We focus on the functoriality properties of these objects. We show that $p$-pseudofunctions are…

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…

We provide a complete description of those Banach algebras that are generated by an invertible isometry of an $L^p$-space together with its inverse. Examples include the algebra $PF_p(\mathbb{Z})$ of $p$-pseudofunctions on $\mathbb{Z}$, the…

We show that a representation of a Banach algebra $A$ on a Banach space $X$ can be extended to a canonical representation of $A^{**}$ on $X$ if and only if certain orbit maps $A\to X$ are weakly compact. When this is the case, we show that…

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…

We define spatial $L^p$ AF algebras for $p \in [1, \infty) \setminus \{ 2 \}$, and prove the following analog of the Elliott AF algebra classification theorem. If $A$ and $B$ are spatial $L^p$ AF algebras, then the following are equivalent:…

For $d = 2, 3, \ldots$ and $p \in [1, \infty),$ we define a class of representations $\rho$ of the Leavitt algebra $L_d$ on spaces of the form $L^p (X, \mu),$ which we call the spatial representations. We prove that for fixed $d$ and $p,$…

Our main result is that the simple Lie group $G=Sp(n,1)$ acts properly isometrically on $L^p(G)$ if $p>4n+2$. To prove this, we introduce property $({\BP}_0^V)$, for $V$ be a Banach space: a locally compact group $G$ has property…

Let $(X,\mathcal{B},\mu)$ be a measure space and $A$ be a norm closed subalgebra of $\mathcal{B}(L^p(X,\mu))$, where $p\in [1,\infty)$. Let $(G,A,\alpha)$ be an $L^p$-operator algebra dynamical system, where $G$ is a countable discrete…

Let G be a discrete group. Suppose that the reduced group C*-algebra of G is simple. We use results of Kalantar-Kennedy and Haagerup, and Banach space interpolation, to prove that, for p in (1,infinity), the reduced group L^p operator…

For $p \in [1, \infty),$ we define and study full and reduced crossed products of algebras of operators on $\sigma$-finite $L^p$ spaces by isometric actions of second countable locally compact groups. We give universal properties for both…

For $p\in (1,\infty)$, we study representations of \'etale groupoids on $L^{p}$-spaces. Our main result is a generalization of Renault's disintegration theorem for representations of \'etale groupoids on Hilbert spaces. We establish a…

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 continue the study of $L^p$-operator algebras associated with directed graphs initiated by Corti\~nas and Rodr\'iguez, and we establish $L^p$-analogs of both the gauge-invariant and the Cuntz-Krieger uniqueness theorems. The first of…

Non-commutative $L^p$-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For $p\geq 2$ they are also proved to possess a {\em sufficient} family of bounded positive sesquilinear forms…

Given a locally compact group $G$, a nondegenerate Banach algebra $A$ with a contractive approximate identity, a twisted action $(\alpha, \sigma)$ of $G$ on $A$, and a family $\mathcal{R}$ of uniformly bounded representations of $A$ on…

We introduce Banach algebras associated to twisted \'etale groupoids $(\mathcal{G},\mathcal{L})$ and to twisted inverse semigroup actions. This provides a unifying framework for numerous recent papers on $L^p$-operator algebras and the…

We construct a crossed product Banach algebra from a Banach algebra dynamical system $(A,G,\alpha)$ and a given uniformly bounded class $R$ of continuous covariant Banach space representations of that system. If $A$ has a bounded left…