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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization of minimal homogeneous Banach spaces
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by Hans G. Feichtinger PDF
Proc. Amer. Math. Soc. 81 (1981), 55-61 Request permission

Abstract:

Let $G$ be a locally compact group. It is shown that for a homogeneous Banach space $B$ on $G$ satisfying a slight additional condition there exists a minimal space ${B_{\min }}$ in the family of all homogeneous Banach spaces which contain all elements of $B$ with compact support. Two characterizations of ${B_{\min }}$ are given, the first one in terms of "atomic" representations. The equivalence of these two characterizations is derived by means of certain (bounded) partitions of unity which are of interest for themselves.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 81 (1981), 55-61
  • MSC: Primary 43A15; Secondary 46H25
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0589135-9
  • MathSciNet review: 589135