Uniform approximation by elementary operators

TL;DR

This paper characterizes when bounded maps preserving ideals in certain C*-algebras can be uniformly approximated by elementary operators, linking this property to the algebra's structure as a sum of specific C*-bundles.

Contribution

It provides a precise structural criterion for uniform approximation by elementary operators in separable C*-algebras.

Findings

Approximation by elementary operators occurs iff the algebra is a finite sum of C*-bundles of finite type.

The result characterizes the structure of C*-algebras allowing such approximations.

The paper establishes a necessary and sufficient condition for uniform approximation in this context.

Abstract

On a separable C*-algebra A every (completely) bounded map, which preserves closed two sided ideals, can be approximated uniformly by elementary operators if and only if A is a finite direct sum of C*-algebras of continuous sections vanishing at infinity of locally trivial C*-bundles of finite type.