Synthetic properties of locally compact groups: preservation and transference

Using techniques from TRO equivalence of masa bimodules we prove various transference results: We show that when \(\alpha\) is a group homomorphism which pushes forward the Haar measure of \(G\) to a measure absolutely continuous with respect to the Haar measure on \(H\), then \((\alpha\times\alpha)...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2021-11
Main Authors: Anoussis, M, Eleftherakis, G K, Katavolos, A
Format: Article
Language:English
Subjects:
Homomorphisms
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Using techniques from TRO equivalence of masa bimodules we prove various transference results: We show that when \(\alpha\) is a group homomorphism which pushes forward the Haar measure of \(G\) to a measure absolutely continuous with respect to the Haar measure on \(H\), then \((\alpha\times\alpha)^{-1}\) preserves sets of compact operator synthesis, and conversely when \(\alpha\) is onto. We also prove similar preservation results for operator Ditkin sets and operator M-sets, obtaining preservation results for M-sets as corollaries. Some of these results extend or complement existing results of Ludwig, Shulman, Todorov and Turowska.
ISSN:2331-8422
DOI:10.48550/arxiv.2111.12005