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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

REFERENCES

1.Berberian, S. K.An extension of Weyl's theorem to a class of not necessarily normal operators, Michigan Math. J. 16 (1969), 273–279.CrossRefGoogle Scholar
2.Berberian, S. K.The Weyl spectrum of an operator, Indiana Univ. Math. J. 20 (1971), 529–544.CrossRefGoogle Scholar
3.Brown, A. and Pearcy, C.Spectra of tensor products of operators, Proc. Amer. Math. Soc. 17 (1966), 162–166.CrossRefGoogle Scholar
4.Duggal, B. P., Browder–Weyl theorems, tensor products and multiplications, pre-print (2006).Google Scholar
5.Duggal, B. P. and Kubrusly, C. S.Weyl's theorem for direct sums, Studia Sci. Math. Hungar. 44 (2007), 275–290.Google Scholar
6.Harte, R. and Lee, W. Y.Another note on Weyl's theorem, Trans. Amer. Math. Soc. 349 (1997), 2115–2124.CrossRefGoogle Scholar
7.Ichinose, T.Spectral properties of linear operators I, Trans. Amer. Math. Soc. 235 (1978), 75–113.CrossRefGoogle Scholar
8.Kubrusly, C. S.Elements of operator theory, (Birkhäuser, 2001).CrossRefGoogle Scholar
9.Kubrusly, C. S.A concise introduction to tensor product, Far East J. Math. Sci. 22 (2006), 137–174.Google Scholar
10.Song, Y.-M. and Kim, A.-H., Weyl's theorem for tensor products, Glasgow. Math. J. 46 (2004), 301–304.CrossRefGoogle Scholar
11.Weidmann, J.Linear operators in Hilbert spaces, (Springer, Verlag, 1980).CrossRefGoogle Scholar