Diagonals of operators and Blaschke’s enigma

Müller, Vladimir; Tomilov, Yuri

doi:10.1090/tran/7804

Diagonals of operators and Blaschke’s enigma
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by Vladimir Müller and Yuri Tomilov PDF

Trans. Amer. Math. Soc. 372 (2019), 3565-3595 Request permission

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.

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