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Transactions of the American Mathematical Society

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Operators on tensor products of Banach spaces


Author: Takashi Ichinose
Journal: Trans. Amer. Math. Soc. 170 (1972), 197-219
MSC: Primary 47A60
MathSciNet review: 0322553
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Abstract: The present paper is a study of operators on tensor products of Banach spaces with the notion of maximal extensions introduced by G. Köthe such that the closure of a closable operator is its unique maximal extension. For a class of such operators the spectral mapping theorem is established. The results apply to the operator $ A \otimes I + I \otimes B$ and give a new meaning to the method of separation of variables.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0322553-1
Keywords: Topological tensor products, operators on tensor products, spectral mapping theorem, spectrum, separation of variables
Article copyright: © Copyright 1972 American Mathematical Society