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| Home > Articles > Published articles > Homogenous Banach spaces on the unit circle |
| Date: | 2000 |
| Abstract: | 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. |
| Rights: | Tots els drets reservats.  |
| Language: | Anglès |
| Document: | Article ; recerca ; Versió publicada |
| Published in: | Publicacions matemàtiques, V. 44 N. 1 (2000) , p. 135-155, ISSN 2014-4350 |
