Thompson's theorem for II_1 factors

TL;DR

This paper extends Thompson's theorem, originally for matrices, to the setting of II_1 factors, providing a new characterization of diagonals given singular values in this advanced mathematical context.

Contribution

It introduces an analogue of Thompson's theorem for II_1 factors, broadening the theorem's applicability to operator algebras.

Findings

Established a Thompson-type theorem for II_1 factors.

Characterized possible diagonals of operators with given singular values.

Extended classical matrix results to infinite-dimensional operator algebras.

Abstract

A theorem of Thompson provides a non-self-adjoint variant of the classical Schur-Horn theorem by characterizing the possible diagonal values of a matrix with given singular values. We prove an analogue of Thompson's theorem for II_1 factors.