Uniqueness of complete norms for quotients of Banach function algebras
Studia Mathematica, Tome 106 (1993) no. 3, pp. 289-302
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $L^1(G)$ of a locally compact abelian group (with identity adjoined if Γ is not compact). In such algebras non-semisimple quotients $A(Γ)/\overline{J(E)}$ 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 $Φ_M$.
@article{10_4064_sm_106_3_289_302,
author = {W. G. Bade and },
title = {Uniqueness of complete norms for quotients of {Banach} function algebras},
journal = {Studia Mathematica},
pages = {289--302},
publisher = {mathdoc},
volume = {106},
number = {3},
year = {1993},
doi = {10.4064/sm-106-3-289-302},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-106-3-289-302/}
}
TY - JOUR AU - W. G. Bade AU - TI - Uniqueness of complete norms for quotients of Banach function algebras JO - Studia Mathematica PY - 1993 SP - 289 EP - 302 VL - 106 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-106-3-289-302/ DO - 10.4064/sm-106-3-289-302 LA - en ID - 10_4064_sm_106_3_289_302 ER -
%0 Journal Article %A W. G. Bade %A %T Uniqueness of complete norms for quotients of Banach function algebras %J Studia Mathematica %D 1993 %P 289-302 %V 106 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-106-3-289-302/ %R 10.4064/sm-106-3-289-302 %G en %F 10_4064_sm_106_3_289_302
W. G. Bade; . Uniqueness of complete norms for quotients of Banach function algebras. Studia Mathematica, Tome 106 (1993) no. 3, pp. 289-302. doi: 10.4064/sm-106-3-289-302
Cité par Sources :