Centralizers on a super-reflexive Schatten ideal

TL;DR

This paper proves that super-reflexive Schatten ideals, including p-Schatten classes for 1<p<∞, do not admit strictly singular bicentralizers, simplifying previous proofs and clarifying their structure.

Contribution

It provides a straightforward proof that super-reflexive Schatten ideals lack strictly singular bicentralizers, extending to p-Schatten classes.

Findings

No strictly singular bicentralizer exists on super-reflexive Schatten ideals.

The result applies specifically to p-Schatten classes for 1<p<∞.

Simplifies understanding of bicentralizer structure in these operator ideals.

Abstract

We give a simple proof that there is no strictly singular bicentralizer on a super-reflexive Schatten ideal. This result applies, in particular, to the $p$-Schatten class for $1<p<\infty$.