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Characterization of homogeneous spaces and their norms

Ward, J. (1984) Characterization of homogeneous spaces and their norms. Pacific Journal of Mathematics, 114 (2). pp. 481-495.

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Let G denote a compact group and B a homogeneous Banach space of pseudomeasures over G (B is left translation invariant with continuous shifts). If T(G) is the linear space of trigonometric polynomials defined on G then T(G) ∩ B is a dense subspace of B. An explicit description is given of T(G) ∩ B. A complete list of the homogeneous closed subspaces of B is given. Moreover it is shown that B is determined by the set T(G) ∩B and N, the restriction of the B norm to this set. This leads to a complete description of those subsets of T(G) and norms N which determine homogeneous Banach spaces.

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: MSP
Copyright: © 1984 Pacific Journal of Mathematics
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