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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Operators on tensor products of Banach spaces
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by Takashi Ichinose PDF
Trans. Amer. Math. Soc. 170 (1972), 197-219 Request permission


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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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 170 (1972), 197-219
  • MSC: Primary 47A60
  • DOI:
  • MathSciNet review: 0322553