Pinchings and Positive linear maps

TL;DR

This paper uses the pinching theorem to enhance existing theorems on operator diagonals and conditional expectations in Hilbert space operator algebras, providing new insights into sums within unitary orbits.

Contribution

It introduces improved results for conditional expectations onto a masa and operator diagonals using the pinching theorem, advancing the understanding of operator algebra structures.

Findings

Enhanced theorems for conditional expectations onto a masa

Established new results for sums in a unitary orbit

Applied the pinching theorem to operator diagonal problems

Abstract

We employ the pinching theorem, ensuring that some operators A admit any sequence of contractions as an operator diagonal of A, to deduce/improve two recent theorems of Kennedy-Skoufranis and Loreaux-Weiss for conditional expectations onto a masa in the algebra of operators on a Hilbert space. We also get a few results for sums in a unitary orbit.