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Proceedings of the American Mathematical Society

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



A characterization of minimal homogeneous Banach spaces

Author: Hans G. Feichtinger
Journal: Proc. Amer. Math. Soc. 81 (1981), 55-61
MSC: Primary 43A15; Secondary 46H25
MathSciNet review: 589135
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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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Keywords: Homogeneous Banach spaces, Segal algebras, Besov spaces, Banach modules
Article copyright: © Copyright 1981 American Mathematical Society