Nonlinear Centralizers in Homology II. The Schatten classes

TL;DR

This paper investigates the extension spaces of Schatten classes viewed as modules over the algebra of bounded operators, providing insights into their structure and properties in the context of homology.

Contribution

It advances the understanding of nonlinear centralizers by explicitly computing extension spaces for Schatten classes in a module setting.

Findings

Computed the extension spaces for Schatten classes as modules.

Provided new characterizations of nonlinear centralizers in this context.

Enhanced the theoretical framework for homological analysis of operator ideals.

Abstract

The paper computes the spaces of extensions for the Schatten classes when they are regarded in its natural module structure over the algebra of bounded operators on the ground Hilbert space.