Positive operators arising asymptotically from contractions

TL;DR

This paper characterizes positive operators that can be obtained as asymptotic limits of contractions in different operator topologies and explores conditions under which two contractions share the same asymptotic limit.

Contribution

It provides a characterization of positive operators as asymptotic limits of contractions and analyzes when two contractions have identical asymptotic limits.

Findings

Characterization of positive operators as asymptotic limits of contractions.

Conditions for two contractions to have the same asymptotic limit.

Analysis in strong and uniform operator topologies.

Abstract

In this paper we characterize those positive operators which are asymptotic limits of contractions in strong operator topology or uniform topology. We examine the problem when the asymptotic limits of two contractions coincide.