Comptes Rendus
no. 6
Mathematical analysis/Functional analysis
A characterizing property of commutative Banach algebras may not be sufficient only on the invertible elements

Presented by: the Editorial Board

Geethika Sebastian1; Sukumar Daniel1
1 Department of Mathematics, Indian Institute of Techology Hyderabad, Kandi, Sangareddy, Telangana 502285, India
Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 594-596.

In this article, we construct a commutative unital Banach algebra, in which the property ‖a2‖=‖a‖2 is true for the invertible elements, but cannot be extended to the whole algebra.

Dans cette Note, nous construisons une algèbre de Banach unitaire, commutative, dans laquelle l'identité ‖a2‖=‖a‖2 est vraie pour les éléments inversibles, mais ne peut être étendue à toute l'algèbre.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.05.002

Geethika Sebastian 1; Sukumar Daniel 1

1 Department of Mathematics, Indian Institute of Techology Hyderabad, Kandi, Sangareddy, Telangana 502285, India 
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Geethika Sebastian; Sukumar Daniel. A characterizing property of commutative Banach algebras may not be sufficient only on the invertible elements. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 594-596. doi : 10.1016/j.crma.2018.05.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.05.002/

[1] T.W. Dawson; J.F. Feinstein On the denseness of the invertible group in Banach algebras, Proc. Amer. Math. Soc., Volume 131 (2003) no. 9, pp. 2831-2839

[2] M.A. Rieffel Dimension and stable rank in K-theory of C*-algebras, Proc. Lond. Math. Soc., Volume 3 (1983) no. 3, pp. 577-600

[3] G. Robertson On the density of the invertible group in C*-algebra, Proc. Edinb. Math. Soc. (2), Volume 20 (1976), pp. 153-157

[4] G. Sebastian; S. Daniel On the open ball centered at an invertible element of a Banach algebra, Oper. Matrices, Volume 12 (2018) no. 1, pp. 19-25

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