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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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Characterization of precompact maps, Schwartz spaces and nuclear spaces
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by Dan Randtke PDF
Trans. Amer. Math. Soc. 165 (1972), 87-101 Request permission

Abstract:

A general representation theorem for “precompact” seminorms on a locally convex space is proven. Using this representation theorem the author derives a representation theorem for precompact maps from one locally convex space into another, that is analogous to the spectral representation theorem for compact maps from one Hilbert space into another and that is applicable to a very extensive class of locally convex spaces. The author uses his representation theorem to derive new characterizations of Schwartz spaces and proves analogous results for nuclear and strongly nuclear spaces.
References
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 165 (1972), 87-101
  • MSC: Primary 46A05; Secondary 47B10
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0305009-1
  • MathSciNet review: 0305009