Crossed product duality for partial $C^*$-automorphisms

TL;DR

This paper investigates the duality properties of crossed products arising from partial automorphisms of C*-algebras, highlighting the failure of Takai-Takesaki duality when these automorphisms are not full automorphisms.

Contribution

It provides new insights into the conditions under which crossed product duality holds or fails for partial automorphisms of C*-algebras.

Findings

Duality tends to fail for partial automorphisms that are not full automorphisms.

The extent of failure correlates with how much the partial automorphism deviates from being an automorphism.

The paper characterizes conditions affecting the duality in the context of partial automorphisms.

Abstract

For partial automorphisms of $C^*$-algebras, Takai-Takesaki crossed product duality tends to fail, in proportion to the extent to which the partial automorphism is not an automorphism.