Homogenous Banach spaces on the unit circle.

Pedersen, 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 -