We prove that every quotient algebra of a unital Banach function algebra A has a unique complete norm if A is a Ditkin algebra. The theorem applies, for example, to the algebra A (Γ) of Fourier transforms of the group algebra of a locally compact abelian group (with identity adjoined if Γ is not compact). In such algebras non-semisimple quotients arise from closed subsets E of Γ which are sets of non-synthesis. Examples are given to show that the condition of Ditkin cannot be relaxed. We construct a variety of mutually non-equivalent norms for quotients of the Mirkil algebra M, which fails Ditkin’s condition at only one point of .
@article{bwmeta1.element.bwnjournal-article-smv106i3p289bwm,
author = {W. Bade and H. Dales},
title = {Uniqueness of complete norms for quotients of Banach function algebras},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {289-302},
zbl = {0811.46050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv106i3p289bwm}
}
Bade, W.; Dales, H. Uniqueness of complete norms for quotients of Banach function algebras. Studia Mathematica, Tome 104 (1993) pp. 289-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv106i3p289bwm/
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