Isometries between groups of invertible elements in $C^{*}$-algebras

TL;DR

This paper characterizes all surjective isometries between open subgroups of invertible elements in unital $C^{*}$-algebras, providing a comprehensive understanding of their structure.

Contribution

It offers a complete description of surjective isometries between open subgroups of invertible elements in unital $C^{*}$-algebras, a topic not fully explored before.

Findings

All surjective isometries are characterized explicitly.

The structure of isometries depends on algebraic and topological properties.

Results extend previous partial classifications in $C^{*}$-algebra theory.

Abstract

In this paper we describe all surjective isometries between open subgroups of the groups of invertible elements in unital $C^{*}$-algebras.