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

Sebastian, Geethika1; Daniel, Sukumar1
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.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2018.05.002
Sebastian, Geethika 1; Daniel, Sukumar 1

1 Department of Mathematics, Indian Institute of Techology Hyderabad, Kandi, Sangareddy, Telangana 502285, India 
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     title = {A characterizing property of commutative {Banach} algebras may not be sufficient only on the invertible elements},
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Sebastian, Geethika; Daniel, Sukumar. 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://www.numdam.org/articles/10.1016/j.crma.2018.05.002/

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

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

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

[4] Sebastian, G.; Daniel, S. 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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