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Weyl Spectral Identity and Biquasitriangularity

Published online by Cambridge University Press:  29 October 2015

C. S. Kubrusly  and
B. P. Duggal
C. S. Kubrusly
Affiliation:
Catholic University of Rio de Janeiro, 22453-900, Rio de Janeiro, Brazil ([email protected])
B. P. Duggal
Affiliation:
University of Niš, Department of Mathematics, PO Box 224, Niš, Serbia ([email protected])
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Abstract

Let A and B be operators acting on infinite-dimensional complex Banach spaces. We say that the Weyl spectral identity holds for the tensor product A⊗B if σw(A⊗B) = σw(A)·σ(B)∪σ(A)·σw(B), where σ(·) and σw(·) stand for the spectrum and the Weyl spectrum, respectively. Conditions on A and B for which the Weyl spectral identity holds are investigated. Especially, it is shown that if A and B are biquasitriangular (in particular, if the spectra of A and B have empty interior), then the Weyl spectral identity holds. It is also proved that if A and B are biquasitriangular, then the tensor product A ⊗ B is biquasitriangular.

Keywords

tensor productWeyl spectral identitybiquasitriangular operatorsPrimary 47A80Secondary 47A53
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 363 - 375
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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