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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Spectral properties of tensor products of linear operators. I


Author: Takashi Ichinose
Journal: Trans. Amer. Math. Soc. 235 (1978), 75-113
MSC: Primary 47A10
DOI: https://doi.org/10.1090/S0002-9947-1978-0472915-2
MathSciNet review: 472915
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Abstract: The aim of the present paper is to obtain, for tensor products of linear operators, their essential spectra in the sense of F. E. Browder, F. Wolf and M. Schechter and explicit formulae of their nullity, deficiency and index. The theory applies to $ A \otimes I + I \otimes B$ and $ A \otimes B$.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0472915-2
Keywords: Topological tensor products, operators on tensor products of Banach spaces, separation of variables, spectral mapping theorem, spectrum, essential spectrum, Fredholm operator, nullity, deficiency and index of operators
Article copyright: © Copyright 1978 American Mathematical Society