On regularity of compressions and diagonals of operator functions

TL;DR

This paper extends classical results on operator compressions and diagonals to time-dependent and smooth operator-valued functions, introducing new techniques especially for selfadjoint operators.

Contribution

It introduces novel results on the regularity of compressions and diagonals of operator functions, with new methods applicable to smooth and time-dependent cases.

Findings

Results for time-dependent operator functions

New techniques for analyzing operator diagonals

Special insights for selfadjoint operators

Abstract

Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no analogues in the literature and rely on a new technique. The results are especially transparent for selfadjoint operators.