相关论文: Isomorphisms of Algebras of Convolution Operators

There is no systematic general procedure by which isomorphism classes of Hopf algebras that are extensions of $\k F$ by ${\k}^G$ can be found. We develop the general procedure for classification of isomorphism classes of Hopf algebras which…

The paper deals with weighted spaces $L_p^w(G)$ on a locally compact group G. If w is a positive measurable function on G then we define the space $L_p^w(G)$, $p\ge1$, as $L_p^w(G)=\{f:fw\in L_p(G)\}$. We consider weights such that these…

We show that the Beurling algebra with a weight-dependent convolution and the group algebra $L^1(G)$ are isomorphic. In particular, using this isomorphism, we extend some results of the algebra $\mathscr{L}^1(G,\omega)$ presented in recent…

The vertex algebras $V^{(p)}$ and $R^{(p)}$ introduced in [2] are very interesting relatives of the famous triplet algebras of logarithmic CFT. The algebra $V^{(p)}$ (respectively, $R^{(p)}$) is a large extension of the simple affine vertex…

I present a general theory of overconvergent p-adic automorphic forms and eigenvarieties for connected reductive algebraic groups G whose real points are compact modulo centre, extending earlier constructions due to Buzzard, Chenevier and…

The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…

A topological group $G$ is called extremely amenable if every continuous action of $G$ on a compact space has a fixed point. This concept is linked with geometry of high dimensions (concentration of measure). We show that a von Neumann…

This paper gives a complete selfcontained proof of our result announced in hep-th/9909126 showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on…

We extend the decomposition conjecture to 2d quantum field theories with a gauged $\text{Rep}(H)$ symmetry category for $H$ a finite-dimensional semisimple Hopf algebra with $\text{Rep}(G)$ trivially-acting and $\text{Vec}(\Gamma)$ the…

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C$^*$-algebra. This implies that the weakly almost periodic functionals on $M(G)$, the measure…

For $1<p<\infty$, we prove (i) a version of Voiculescu's absorption theorem for operators on $l^{p}$, (ii) that $\mathrm{Ext}_{\sim,s}(\mathcal{A},K(l^{p}))$ is a group for certain Banach algebra $\mathcal{A}$, and (iii) homotopy invariance…

In this paper, for $p\in(1,\infty)$ we study $p$-complete boundedness of weighted homomorphisms on the $p$-analog of the Fourier-Stieltjes algebras, $B_p(G)$, based on the $p$-operator space structure defined by the authors. Here, for a…

In the line of previous work by Naor, we establish new forms of metric $\mathrm{X}_p$ inequalities in group algebras under very general assumptions. Our results' applicability goes beyond the previously known setting in two directions. In…

Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$. It is shown that, if $\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\mu)$ such that the Banach space…

Without using the $p$-adic Langlands correspondence, we prove that for many finite length smooth representations of $\mathrm{GL}_2(\mathbf{Q}_p)$ on $p$-torsion modules the $\mathrm{GL}_2(\mathbf{Q}_p)$-linear morphisms coincide with the…

We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…

Let $G$ be a direct product of inner forms of general linear groups over non-archimedean locally compact fields of residue characteristic $p$ and let $K^1$ be the pro-$p$-radical of a maximal compact open subgroup of $G$. In this paper we…

To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…

Suppose that G is a connected reductive group over a p-adic field F, that K is a hyperspecial maximal compact subgroup of G(F), and that V is an irreducible representation of K over the algebraic closure of the residue field of F. We…

We prove that if the group of isometries of C(X,E) is algebraically reflexive, then the group of n-isometries is also algebraically reflexive. Here, X is a compact Hausdorff space and E is a Banach space. As a corollary to this, we…