Journal article
Characterization of homogeneous spaces and their norms
Pacific Journal of Mathematics, Vol.114(2), pp.481-495
1984
Abstract
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.
Details
- Title
- Characterization of homogeneous spaces and their norms
- Authors/Creators
- J. Ward (Author/Creator)
- Publication Details
- Pacific Journal of Mathematics, Vol.114(2), pp.481-495
- Publisher
- MSP
- Identifiers
- 991005543347407891
- Copyright
- © 1984 Pacific Journal of Mathematics
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
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- Citation topics
- 9 Mathematics
- 9.28 Pure Maths
- 9.28.886 Operator Algebras
- Web Of Science research areas
- Mathematics
- ESI research areas
- Mathematics