Unconditional Integrability for Dual Actions

TL;DR

This paper establishes an integrability property for dual actions of locally compact abelian groups within C*-algebraic bundles, extending existing concepts with new tools like a generalized Bochner integral and Fourier inversion for operator-valued functions.

Contribution

It introduces a novel integrability property for dual actions and develops generalized analytical tools applicable to operator-valued maps in the context of C*-algebraic bundles.

Findings

Dual actions satisfy a new integrability property

Generalized Bochner integral for operator-valued functions

Fourier inversion formula for operator-valued maps

Abstract

The dual action of a locally compact abelian group, in the context of C*-algebraic bundles, is shown to satisfy an integrability property, similar to Rieffel's proper actions. The tools developed include a generalization of Bochner's integral as well as a Fourier inversion formula for operator valued maps.