Diagonals of operators and Blaschke's enigma

2018/05/21 by Muller, Vladimir, Tomilov, Yuri · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1805.08188

Abstract

We introduce new techniques allowing one to construct diagonals of bounded Hilbert space operators and operator tuples under "Blaschke-type" assumptions. This provides a new framework for a number of results in the literature and identifies, often large, subsets in the set of diagonals of arbitrary bounded operators (and their tuples). Moreover, our approach leads to substantial generalizations of the results due to Bourin, Herrero and Stout having assumptions of a similar nature.

Cited by

• On regularity of compressions and diagonals of operator functions
• The numerical ranges of the generalized quadratic operators

Related

• Diagonals of self-adjoint operators I: compact operators
• On interplay between operators, bases, and matrices
• Diagonals of self-adjoint operators II: Non-compact operators
• Schauder Bases and Operator Theory
• Matrix representations of arbitrary bounded operators on Hilbert spaces