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Transactions of the American Mathematical Society

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

 

 

Compact functors and their duals in categories of Banach spaces


Author: Kenneth L. Pothoven
Journal: Trans. Amer. Math. Soc. 155 (1971), 149-159
MSC: Primary 08.10
DOI: https://doi.org/10.1090/S0002-9947-1971-0280425-4
MathSciNet review: 0280425
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Abstract: In a recent paper, B. S. Mityagin and A. S. Shvarts list many problems concerning functors and dual functors in categories of Banach spaces. Included in these problems is the question: What properties characterize compact functors? The purpose of this paper is to give partial answers to that question. Partial characterizations are given in terms of what are called Fredholm functors and finite rank functors. Affirmative answers are also given to two other questions of Mityagin and Shvarts. They are (1) If a functor is compact, is its dual compact? (2) If a natural transformation is compact, is its dual compact?


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DOI: https://doi.org/10.1090/S0002-9947-1971-0280425-4
Keywords: Compact functors, categories of Banach spaces, projective tensor product, weakly compact natural transformations, Fredholm functor, finite rank functor, approximation property
Article copyright: © Copyright 1971 American Mathematical Society