Related papers: On Convolution Dominated Operators

If $G$ is a locally compact group, $CD(G)$ the algebra of convolution dominated operators on $L^2(G)$ then an important question is: Is $\mathbb{C}1+CD(G)$ (respectively $CD(G)$ if $G$ is discrete) inverse-closed in the bounded operators on…

We study infinite matrices $A$ indexed by a discrete group $G$ that are dominated by a convolution operator in the sense that $|(Ac)(x)| \leq (a \ast |c|)(x)$ for $x\in G$ and some $a\in \ell ^1(G)$. This class of "convolution-dominated"…

By relating notions from quantum harmonic analysis and band-dominated operator theory, we prove that over any locally compact abelian group $G$, the operator algebra $\mathcal C_1$ from quantum harmonic analysis agrees with the intersection…

A discrete group $\G$ is called rigidly symmetric if the projective tensor product between the convolution algebra $\ell^1(\G)$ and any $C^*$-algebra $\A$ is symmetric. We show that in each topologically graded $C^*$-algebra over a rigidly…

We show that a regular locally compact quantum group $\mathbb{G}$ is discrete if and only if $L^\infty(\mathbb{G})$ contains non-zero compact operators on $L^2(\mathbb{G})$. As a corollary we classify all discrete quantum groups among…

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 study algebraic properties on a group G such that if the discrete group G has these properties then every locally compact shift continuous topology on G with adjoined zero is either compact, or discrete. We introduce electorally flexible…

Let ${\Bbb G}$ be a locally compact quantum group and ${\mathcal T}(L^2({\Bbb G}))$ be the Banach algebra of trace class operators on $L^2({\Bbb G})$ with the convolution induced by the right fundamental unitary of ${\Bbb G}$. We study the…

A discrete group $\G$ is called rigidly symmetric if for every $C^*$-algebra $\A$ the projective tensor product $\ell^1(\G)\widehat\otimes\A$ is a symmetric Banach $^*$-algebra. For such a group we show that the twisted crossed product…

Let $G$ be a discrete group, let $p\ge1$, and let $\omega$ be a weight on $G$. Using the approach from [9], we provide sufficient conditions on a weight $\omega$ for $\ell^p(G,\omega)$ to be a Banach algebra admitting a norm-controlled…

Flag kernels are tempered distributions which generalize these of Calderon-Zygmund type. For any homogeneous group $\mathbb{G}$ the class of operators which acts on $L^{2}(\mathbb{G})$ by convolution with a flag kernel is closed under…

Let $({\sf G},\alpha, \omega,\mathfrak B)$ be a measurable twisted action of the locally compact group ${\sf G}$ on a Banach $^*$-algebra $\mathfrak B$ and $\mathfrak A$ a differential Banach $^*$-subalgebra of $\mathfrak B$, which is…

We prove that, given a discrete group $G$, and $1 \leq p < \infty$, the algebra of $p$-convolution operators $CV_p(G)$ is weak*-simple, in the sense of having no non-trivial weak*-closed ideals, if and only if $G$ is an ICC group. This…

We present an intrinsically defined algebra of operators containing the right and left invariant Calder\'on-Zygmund operators on a stratified group. The operators in our algebra are pseudolocal and bounded on L^p (1<p<\infty). This algebra…

In this paper we will study the isomorphism problem for the reduced twisted group and groupoid $L^p$-operator algebras. For a locally compact group $G$ and a continuous 2-cocycle $\sigma$ we will define the reduced $\sigma$-twisted…

We say that a tempered distribution $A$ belongs to the class $S^m(\Ge)$ on a homogeneous Lie algebra $\Ge$ if its Abelian Fourier transform $a=\hat{A}$ is a smooth function on the dual $\Ges$ and satisfies the estimates $$…

We prove two theorems about convolution operators on $L^p(G)$ for a locally compact group $G$. First, if $G$ has the approximation property, then the algebra of convoluters is the algebra of pseudo-measures. Second, the bicommutant of the…

Let $\Gamma$ be a finitely generated discrete exact group. We consider operators on $l^2(\Gamma)$ which are composed by operators of multiplication by a function in $l^\infty (\Gamma)$ and by the operators of left-shift by elements of…

We consider the {\it concentration functions problem} for discrete quantum groups; we prove that if $\mathbb{G}$ is a discrete quantum group, and $\mu$ is an irreducible state in $l^1(\mathbb{G})$, then the convolution powers $\mu^n$,…

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…