On Mean Ergodic Convergence in the Calkin Algebras

TL;DR

This paper provides a geometric characterization of mean ergodic convergence within Calkin algebras for Banach spaces possessing the bounded compact approximation property, advancing understanding of operator behavior in these algebras.

Contribution

It introduces a new geometric criterion for mean ergodic convergence in Calkin algebras, specifically for Banach spaces with the bounded compact approximation property.

Findings

Characterizes mean ergodic convergence geometrically in Calkin algebras.

Applies to Banach spaces with the bounded compact approximation property.

Enhances understanding of operator convergence in functional analysis.

Abstract

In this paper, we give a geometric characterization of mean ergodic convergence in the Calkin algebras for Banach spaces that have the bounded compact approximation property.