The Bridge Lemmas between Equivalent Fell Bundles and its Applications

TL;DR

This paper establishes the equivalence of induced representation theories for two Fell bundles and extends these results to broader classes, enhancing the understanding of their structure and applications in operator algebra theory.

Contribution

It proves the equivalence of induced representation theories for equivalent Fell bundles and generalizes imprimitivity theorems to all Fell bundles.

Findings

Induced representation theories are essentially identical for equivalent Fell bundles.

Results extend imprimitivity theorems to arbitrary Fell bundles.

Provides foundational tools for analyzing Fell bundle representations.

Abstract

In this paper, we prove that the induced representation theories of two equivalent Fell bundles are essentially identical; and we apply our results to carry the induced representation theory and imprimitivity theorems of saturated Fell bundles to arbitrary Fell bundles.