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Homogenous Banach spaces on the unit circle
Pedersen, Thomas Vils

Data: 2000
Resum: We prove that a homogeneous Banach space ß on the unit circle T can be embedded as a closed subspace of a dual space [Xi]*ß contained in the space of bounded Borel measures on T in such a way that the map ß --> [Xi]*ß defines a bijective correspondence between the class of homogeneous Banach spaces on T and the class of prehomogeneous Banach spaces on T. We apply our results to show that the algebra of all continuous functions on T is the only homogeneous Banach algebra on T in which every closed ideal has a bounded approximate identity with a common bound, and that the space of multipliers between two homogeneous Banach spaces is a dual space. Finally, we describe the space [Xi]*ß for some examples of homogeneous Banach spaces ß on T.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Publicat a: Publicacions matematiques, V. 44 N. 1 (2000) , p. 135-155, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_44100_04

21 p, 205.6 KB

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