Thompson's theorem for compact operators and diagonals of unitary operators

TL;DR

This paper extends Thompson's theorem to compact operators and characterizes diagonals of unitary operators, utilizing key inequalities and classical theorems in operator theory.

Contribution

It introduces an extension of Thompson's theorem to compact operators and provides a new characterization of unitary operator diagonals.

Findings

Extended Thompson's theorem to compact operators

Characterized diagonals of unitary operators

Utilized Thompson's inequality in new contexts

Abstract

As applications of Kadison's Pythageorean and carpenter's theorems, the Schur-Horn theorem, and Thompson's theorem, we obtain an extension of Thompsons theorem to compact operators and use these ideas to give a characterization of diagonals of unitary operators. Thompson's mysterious inequality concerning the last terms of the diagonal and singular value sequences plays a central role.