Some functorial properties of Schatten classes

TL;DR

This paper explores the functorial properties of Schatten classes within the context of $C^*$-algebras and group representations, providing insights into their structural behavior and mappings.

Contribution

It introduces new functorial properties of Schatten classes in the categories of $C^*$-algebra representations and group unitary representations.

Findings

Identifies conditions under which elements map to Schatten class ideals

Establishes functorial relationships between $C^*$-algebra representations and Schatten classes

Provides a framework for understanding Schatten classes in representation categories

Abstract

In this paper, we begin with the study of elements in $C^*$-algebras which are mapped to Schatten class ideals through faithful left regular representation. We further give some functorial properties of Schatten classes on the category of representations of a $C^*$-algebra and category of unitary representations of a group.