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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2018: 0.29

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1337-2211
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Volume 69, Issue 2

Issues

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

Abstract

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

References

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    Simon, B: Trace Ideals and Their Applications. Math. Surveys Monogr. 120, Providence, RI, 2005.Google Scholar

  • [2]

    Voiculescu, D. V.: Hilbert space operators modulo normed ideals, In: Proc. Int. Congr. Math., 1983. Warszawa, pp. 1041–1047.Google Scholar

  • [3]

    Voiculescu, D. V.: Almost normal operators mod Hilbert-Schmidt and the K-theory of the algebras EΛ(Ω), J. Noncommut. Geom. 8 (2014), 1123–1145.CrossrefWeb of ScienceGoogle Scholar

  • [4]

    Voiculescu, D. V.: Some results on norm-ideal perturbations of Hilbert space operators II, J. Operator Theory 5 (1981), 77–100.Google Scholar

  • [5]

    Voiculescu, D. V.: On the existence of quasicentral approximate units relative to normed ideals. Part I J. Funct. Anal. 91 (1990), 1–36.CrossrefGoogle Scholar

  • [6]

    Weiss G., The Fuglede commutativity theorem modulo operator ideals, Proc. Amer. Math. Soc. 83 (1981), 113–118.CrossrefGoogle Scholar

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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