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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

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Volume 69, Issue 2


Some consequences of quasicentral approximate units modulo Hilbert-Schmidt class

Vasile Lauric
Published Online: 2019-03-19 | DOI: https://doi.org/10.1515/ms-2017-0235


Conjecture 4 of Voiculescu implies that almost normal operators must satisfy a Fuglede-Putnam theorem, namely [T, X] is a Hilbert-Schmidt operator whenever [T, X] is in the same class for an arbitrary operator X. In this note, a partial answer to this question is given, namely when X ∈ 𝓒4, the Fuglede-Putnam theorem holds.

MSC 2010: Primary 47B20; 47B37

Keywords: almost normal operators; quasicentral approximate units


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About the article

To the memory of my grandmother, Maria

Received: 2018-02-17

Accepted: 2018-04-16

Published Online: 2019-03-19

Published in Print: 2019-04-24

(Communicated by Werner Timmermann)

Citation Information: Mathematica Slovaca, Volume 69, Issue 2, Pages 433–436, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0235.

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