The Topology of Uniform Convergence on a Group Is Discrete for Unitary Representations of Amenable Groups

IF 1.5 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI:10.1134/S1061920825020153

A.I. Shtern

引用次数: 0

Abstract

We prove that a unitary representation \(\rho\) of an amenable locally compact group \(G\) such that \(\|\rho(g)-\pi(g)\|\le q<1/2\) for all \(g\in G\) and for some continuous unitary representation \(\pi\) of \(G\) in the same Hilbert space is unitary equivalent to \(\pi\).

DOI 10.1134/S1061920825020153

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对于可服从群的幺正表示，群上一致收敛的拓扑是离散的

我们证明了一个可服从的局部紧群\(G\)的酉表示\(\rho\)使得\(\|\rho(g)-\pi(g)\|\le q<1/2\)对于所有的\(g\in G\)和对于同一Hilbert空间中\(G\)的连续酉表示\(\pi\)是酉等价于\(\pi\)的。Doi 10.1134/ s1061920825020153

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.