A characterization of minimal homogeneous Banach spaces

Feichtinger, Hans G.

doi:10.1090/S0002-9939-1981-0589135-9

A characterization of minimal homogeneous Banach spaces
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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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