Transference and preservation of uniqueness

TL;DR

This paper explores the concept of uniqueness in the Fourier algebra of locally compact groups, establishing a connection with operator bimodules and demonstrating the stability of this property under various operations.

Contribution

It introduces and studies ideals of uniqueness in the Fourier algebra and their operator counterparts, establishing a transference principle and demonstrating property preservation.

Findings

Established a transference between ideals of uniqueness and masa-bimodules.

Proved that the property of being an ideal of uniqueness is preserved under natural operations.

Linked the notion of uniqueness in Fourier algebras to operator bimodules in a rigorous framework.

Abstract

Motivated by the notion of a set of uniqueness in a locally compact group $G$, we introduce and study ideals of uniqueness in the Fourier algebra $A(G)$ of $G$, and their accompanying operator version, masa-bimodules of uniqueness. We establish a transference between the two notions, and use this result to show that the property of being an ideal of uniqueness is preserved under natural operations.