# Homogenous Banach spaces on the unit circle.

Publicacions Matemàtiques (2000)

- Volume: 44, Issue: 1, page 135-155
- ISSN: 0214-1493

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topPedersen, Thomas Vils. "Homogenous Banach spaces on the unit circle.." Publicacions Matemàtiques 44.1 (2000): 135-155. <http://eudml.org/doc/41386>.

@article{Pedersen2000,

abstract = {We prove that a homogeneous Banach space B on the unit circle T can be embedded as a closed subspace of a dual space Ξ*B contained in the space of bounded Borel measures on T in such a way that the map B → Ξ*B 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 Ξ*B for some examples of homogeneous Banach spaces B on T.},

author = {Pedersen, Thomas Vils},

journal = {Publicacions Matemàtiques},

keywords = {Espacios de Banach; Funciones analíticas; Funciones de variación acotada; homogeneous Banach spaces; prehomogeneous Banach spaces; bounded approximate identity; space of multipliers},

language = {eng},

number = {1},

pages = {135-155},

title = {Homogenous Banach spaces on the unit circle.},

url = {http://eudml.org/doc/41386},

volume = {44},

year = {2000},

}

TY - JOUR

AU - Pedersen, Thomas Vils

TI - Homogenous Banach spaces on the unit circle.

JO - Publicacions Matemàtiques

PY - 2000

VL - 44

IS - 1

SP - 135

EP - 155

AB - We prove that a homogeneous Banach space B on the unit circle T can be embedded as a closed subspace of a dual space Ξ*B contained in the space of bounded Borel measures on T in such a way that the map B → Ξ*B 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 Ξ*B for some examples of homogeneous Banach spaces B on T.

LA - eng

KW - Espacios de Banach; Funciones analíticas; Funciones de variación acotada; homogeneous Banach spaces; prehomogeneous Banach spaces; bounded approximate identity; space of multipliers

UR - http://eudml.org/doc/41386

ER -

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