Compressions and Pinchings

TL;DR

This paper explores the existence of operators that can be decomposed into orthogonal projections to represent any sequence of contractions, revealing a structural property of such operators.

Contribution

It introduces a class of operators that can be decomposed into orthogonal projections to model arbitrary contraction sequences.

Findings

Operators can be decomposed into orthogonal projections for any contraction sequence.

The decomposition allows representing contractions as direct sums of operators.

This reveals new structural insights into operator theory.

Abstract

There exist operators $A$ such that : for any sequence of contractions $\{A_n\}$, there is a total sequence of mutually orthogonal projections $\{E_n\}$ such that $\Sigma E_nAE_n=\bigoplus A_n$.