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The Weyl–von Neumann theorem in von Neumann factors

  • Krzysztof Kamiński EMAIL logo
Veröffentlicht/Copyright: 25. Mai 2017

Abstract

In a von Neumann factor of type II with semifinite faithful normal trace τ, the q-th Schatten-type norm q of an operator A is defined as Aq=(τ(|A|q))1q. We will prove that for every self-adjoint operator H and any numbers q>1, ε>0, there exists a self-adjoint perturbation operator A such that A<ε, Aq<ε, and H+A has a pure point spectrum. We will also discuss the possibility of transferring this result onto other von Neumann factors.

Funding statement: The author was partially supported by grant 09/BMN/WN/16 (GMU).

Acknowledgements

I’m very grateful to my Ph.D. advisor, Professor Adam Paszkiewicz from the University of Łódź (Faculty of Mathematics and Computer Science), for the time spent on our discussions and his valuable comments and advices.

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Received: 2016-12-8
Accepted: 2017-4-5
Published Online: 2017-5-25
Published in Print: 2017-6-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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