[Une propriété caractérisant des algèbres de Banach commutatives qui ne peut être formulée sur les seuls éléments inversibles]
Dans cette Note, nous construisons une algèbre de Banach unitaire, commutative, dans laquelle l'identité est vraie pour les éléments inversibles, mais ne peut être étendue à toute l'algèbre.
In this article, we construct a commutative unital Banach algebra, in which the property is true for the invertible elements, but cannot be extended to the whole algebra.
Accepté le :
Publié le :
@article{CRMATH_2018__356_6_594_0, author = {Sebastian, Geethika and Daniel, Sukumar}, title = {A characterizing property of commutative {Banach} algebras may not be sufficient only on the invertible elements}, journal = {Comptes Rendus. Math\'ematique}, pages = {594--596}, publisher = {Elsevier}, volume = {356}, number = {6}, year = {2018}, doi = {10.1016/j.crma.2018.05.002}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2018.05.002/} }
TY - JOUR AU - Sebastian, Geethika AU - Daniel, Sukumar TI - A characterizing property of commutative Banach algebras may not be sufficient only on the invertible elements JO - Comptes Rendus. Mathématique PY - 2018 SP - 594 EP - 596 VL - 356 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2018.05.002/ DO - 10.1016/j.crma.2018.05.002 LA - en ID - CRMATH_2018__356_6_594_0 ER -
%0 Journal Article %A Sebastian, Geethika %A Daniel, Sukumar %T A characterizing property of commutative Banach algebras may not be sufficient only on the invertible elements %J Comptes Rendus. Mathématique %D 2018 %P 594-596 %V 356 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2018.05.002/ %R 10.1016/j.crma.2018.05.002 %G en %F CRMATH_2018__356_6_594_0
Sebastian, Geethika; Daniel, Sukumar. A characterizing property of commutative Banach algebras may not be sufficient only on the invertible elements. Comptes Rendus. Mathématique, Tome 356 (2018) no. 6, pp. 594-596. doi : 10.1016/j.crma.2018.05.002. http://archive.numdam.org/articles/10.1016/j.crma.2018.05.002/
[1] On the denseness of the invertible group in Banach algebras, Proc. Amer. Math. Soc., Volume 131 (2003) no. 9, pp. 2831-2839
[2] Dimension and stable rank in K-theory of C*-algebras, Proc. Lond. Math. Soc., Volume 3 (1983) no. 3, pp. 577-600
[3] On the density of the invertible group in C*-algebra, Proc. Edinb. Math. Soc. (2), Volume 20 (1976), pp. 153-157
[4] On the open ball centered at an invertible element of a Banach algebra, Oper. Matrices, Volume 12 (2018) no. 1, pp. 19-25
Cité par Sources :