Related papers: Classification of $L^p$ AF algebras

In a previous paper, we introduced L^p UHF algebras for p in [1, \infty). We concentrated on the spatial L^p UHF algebras, which are classified up to isometric isomorphism by p and the scaled ordered K_0-group. In this paper, we concentrate…

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…

For a nontrivial locally compact group $G$, and $p\in [1,\infty)$, consider the Banach algebras of $p$-pseudofunctions, $p$-pseudomeasures, $p$-convolvers, and the full group $L^p$-operator algebra. We show that these Banach algebras are…

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 $p,$…

We prove that, for $p \in [1, \infty),$ and integers $d$ at least 2, the $L^p$ analog ${\mathcal{O}}_d^p$ of the Cuntz algebra ${\mathcal{O}}_d$ is a purely infinite simple amenable Banach algebra. The proof requires what we call the…

We study embeddings of $L^p$-operator algebras arising from (twisted) \'etale groupoids, with particular emphasis on rigidity phenomena for $p\neq 2$. Our methods rely on a detailed analysis of core normalizers and their functorial behavior…

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…

For 1 ≤ p < ∞, it is known that the set K^*_p contains of all Lambert multipliers acting between L^p-spaces is a Banach space. In this study, we introduce a new induced norm by conditional expectation operators to show that K^*_p is a…

In this paper, we characterize when the $\ell^p$ uniform Roe algebra of a metric space with bounded geometry is (stably) finite and when it is properly infinite in standard form for $p\in [1,\infty)$. Moreover, we show that the $\ell^p$…

It is shown that all the approximately finite dimensional C*-algebras which are not of Type I are isomorphic as Banach spaces. This generalises the matroid case given previously by Arazy. Analogous results are obtained for various families…

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…

We show that any bounded analytic semigroup on $L^p$ (with $1<p<\infty$) whose negative generator admits a bounded $H^{\infty}$ functional calculus with respect to some angle $< \pi/2$ can be dilated into a bounded analytic semigroup…

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 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 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 $A_p(G)$…

\begin{abstract} Suppose $p$ is a computable real so that $p \geq 1$. It is shown that the halting set can compute a surjective linear isometry between any two computable copies of $\ell^p$. It is also shown that this result is optimal in…

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 compute the operator $p$-norm of some $n\times n$ complex matrices, which can be seen as bounded linear operators on the $n$ dimensional Banach space $\ell^p(n)$. The notion of logarithmic affine matrices is defined, and for such a…

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 that there are $2^{2^{\aleph_0}}$ different closed ideals in the Banach algebra $L(L_p(0,1))$, $1<p\not= 2<\infty$. This solves a problem in A. Pietsch's 1978 book "Operator Ideals". The proof is quite different from other methods…