Compact functors and their duals in categories of Banach spaces

Pothoven, Kenneth L.

doi:10.1090/S0002-9947-1971-0280425-4

Compact functors and their duals in categories of Banach spaces
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by Kenneth L. Pothoven PDF

Trans. Amer. Math. Soc. 155 (1971), 149-159 Request permission

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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Functors in categories of Banach spaces

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