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A characterizing property of commutative Banach algebras may not be sufficient only on the invertible elements

Authors:	Geethika Sebastian Sukumar Daniel

Affiliation:	Department of Mathematics, Indian Institute of Techology Hyderabad, Kandi, Sangareddy, Telangana 502285, India

Abstract:	In this article, we construct a commutative unital Banach algebra, in which the property $6 a^{2} 6 = {6 a 6}^{2}$ is true for the invertible elements, but cannot be extended to the whole algebra.

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