Geodesic
Multipliers with closed range on commutative semisimple Banach algebras
A. Ülger1
1 Department of Mathematics Koc University Fener Yolu 80910, Sariyer, Istanbul, Turkey
Studia Mathematica, Tome 153 (2002) no. 1, pp. 59-80

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $A$ be a commutative semisimple Banach algebra, ${\mit\Delta} (A)$ its Gelfand spectrum, $T$ a multiplier on $A$ and $\widehat{T}$ its Gelfand transform. We study the following problems. (a) When is $\delta (T)=\inf \{| \widehat{T}(f)|:f\in {\mit\Delta} (A)$, $\widehat{T}(f)\neq 0\}>0?$ (b) When is the range $T(A)$ of $T$ closed in $A$ and does it have a bounded approximate identity? (c) How to characterize the idempotent multipliers in terms of subsets of ${\mit\Delta} (A)?$
DOI : 10.4064/sm153-1-5
Keywords: commutative semisimple banach algebra mit delta its gelfand spectrum multiplier widehat its gelfand transform study following problems delta inf widehat mit delta widehat neq range closed does have bounded approximate identity characterize idempotent multipliers terms subsets mit delta

A. Ülger 1

1 Department of Mathematics Koc University Fener Yolu 80910, Sariyer, Istanbul, Turkey 
@article{10_4064_sm153_1_5,
     author = {A. \"Ulger},
     title = {Multipliers with closed range on commutative
 semisimple {Banach} algebras},
     journal = {Studia Mathematica},
     pages = {59--80},
     publisher = {mathdoc},
     volume = {153},
     number = {1},
     year = {2002},
     doi = {10.4064/sm153-1-5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm153-1-5/}
}
TY  - JOUR
AU  - A. Ülger
TI  - Multipliers with closed range on commutative
 semisimple Banach algebras
JO  - Studia Mathematica
PY  - 2002
SP  - 59
EP  - 80
VL  - 153
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm153-1-5/
DO  - 10.4064/sm153-1-5
LA  - en
ID  - 10_4064_sm153_1_5
ER  - 
%0 Journal Article
%A A. Ülger
%T Multipliers with closed range on commutative
 semisimple Banach algebras
%J Studia Mathematica
%D 2002
%P 59-80
%V 153
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm153-1-5/
%R 10.4064/sm153-1-5
%G en
%F 10_4064_sm153_1_5
A. Ülger. Multipliers with closed range on commutative
 semisimple Banach algebras. Studia Mathematica, Tome 153 (2002) no. 1, pp. 59-80. doi: 10.4064/sm153-1-5

Cité par Sources :