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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Diagonals of operators and Blaschke's enigma


Authors: Vladimir Müller and Yuri Tomilov
Journal: Trans. Amer. Math. Soc. 372 (2019), 3565-3595
MSC (2010): Primary 47A20, 47A12, 47A10; Secondary 47B37
DOI: https://doi.org/10.1090/tran/7804
Published electronically: June 3, 2019
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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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Additional Information

Vladimir Müller
Affiliation: Institute of Mathematics, Czech Academy of Sciences, Žitna Street 25, Prague, Czech Republic
Email: muller@math.cas.cz

Yuri Tomilov
Affiliation: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich Street 8, 00-656 Warsaw, Poland
Email: ytomilov@impan.pl

DOI: https://doi.org/10.1090/tran/7804
Keywords: Diagonals, pinchings, dilations, numerical range, spectrum, powers
Received by editor(s): May 21, 2018
Received by editor(s) in revised form: January 8, 2019
Published electronically: June 3, 2019
Additional Notes: This work was partially supported by the NCN grant UMO-2017/27/B/ST1/00078 and by Grant No. 17-27844S of GA CR and RVO:67985840
Article copyright: © Copyright 2019 American Mathematical Society