Synthetic properties of locally compact groups: preservation and transference

Abstract

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.

This article partially replaces arXiv:2104.01657, which has been withdrawn

References in corpus (2)

• Ideals of $A(G)$ and bimodules over maximal abelian selfadjoint algebras
• Crossed products of dual operator spaces and a characterization of groups with the approximation property