Isometric Embeddability of Schatten Classes Revisited

TL;DR

This paper reviews known results and open questions on isometric embeddings between Schatten classes and introduces a new non-embeddability result using a novel approach.

Contribution

It provides a summary of existing knowledge and presents a new non-embeddability theorem for Schatten classes with a novel method.

Findings

Summarizes known results on Schatten class embeddings.

Identifies open questions in isometric embeddability.

Proposes a new non-embeddability result using a novel method.

Abstract

In this note, we summarize known results and open questions on the existence of isometric embeddings between different Schatten classes as well as obtain a new non-embeddability result using a novel method. We also provide a brief overview of the relevant methods.