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.
@article{urn:eudml:doc:41386,
title = {Homogenous Banach spaces on the unit circle.},
journal = {Publicacions Matem\`atiques},
volume = {44},
year = {2000},
pages = {135-155},
mrnumber = {MR1775745},
zbl = {0962.46015},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41386}
}
Pedersen, Thomas Vils. Homogenous Banach spaces on the unit circle.. Publicacions Matemàtiques, Tome 44 (2000) pp. 135-155. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41386/