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ON WEYL AND BROWDER SPECTRA OF TENSOR PRODUCTS

Published online by Cambridge University Press:  01 May 2008

C. S. KUBRUSLY  and
B. P. DUGGAL
C. S. KUBRUSLY
Affiliation:
Catholic University of Rio de Janeiro, 22453-900, Rio de Janeiro, RJ, Brazil e-mail: carlos@ele.puc-rio.br
B. P. DUGGAL
Affiliation:
8 Redwood Grove, Northfields Avenue, Ealing, London W5 4SZ, England, U.K. e-mail: bpduggal@yahoo.co.uk
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Abstract

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Let A and B be Hilbert space operators. In this paper we explore the structure of parts of the spectrum of the tensor product A ⊗ B, and conclude some properties that follow from such a structure. We give conditions on A and B ensuring that σw(A ⊗ B) =σw(A)ċσ(B) ∪ σ(A)ċσw(B), where σ(ċ) and σw(ċ) stand for the spectrum and Weyl spectrum, respectively. We also investigate the problem of transferring Weyl and Browder's theorems from A and B to their tensor product A⊗B.

Keywords

Primary 47A80Secondary 47A53
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 2 , May 2008 , pp. 289 - 302
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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