On regularity of compressions and diagonals of operator functions

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.

This is a version of the paper to appear in Journal of the London Mathematical Society