The Stable Rank of C*-modules

TL;DR

This paper establishes the equality of two notions of stable rank for finitely generated projective modules over unital C*-algebras, introducing a new concept of stable rank for Hilbert modules.

Contribution

It introduces the stable rank of Hilbert modules and proves the equality of topological and Bass stable ranks for certain C*-modules.

Findings

Topological and Bass stable ranks are equal for finitely generated projective modules over unital C*-algebras.

Introduces the concept of stable rank for Hilbert modules.

Provides a new perspective on module stability in operator algebras.

Abstract

We prove equality between the Topological Stable Rank and the Bass Stable Rank for finitely generated projective left modules over a unital C*-algebra. In order to do so, the concept of Stable Rank of a Hilbert module is introduced.