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arXiv · 2111.12005

Synthetic properties of locally compact groups: preservation and transference

M. Anoussis·G. K. Eleftherakis·A. Katavolos
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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.

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M. Anoussis, G. K. Eleftherakis, A. Katavolos. 2021-11-22. Synthetic properties of locally compact groups: preservation and transference. https://doi.org/10.1007/s00605-022-01736-8

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