Bhatt, S. J. ; Dedania, H. V. (1995) Banach algebras in which every element is a Topological zero divisor Proceedings of the American Mathematical Society, 123 (3). pp. 735737. ISSN 00029939

PDF
 Publisher Version
347kB 
Official URL: http://www.ams.org/journals/proc/199512303/S0002...
Related URL: http://dx.doi.org/10.1090/S00029939199512246130
Abstract
Every element of a complex Banach algebra (A, ║ · ║) is a topological divisor of zero, if at least one of the following holds: (i) A is infinite dimensional and admits an orthogonal basis, (ii) A is a nonunital uniform Banach algebra in which the Silov boundary ∂ A coincides with the Gelfand space Δ(A); and (iii) A is a nonunital hermitian Banach ^{*}algebra with continuous involution. Several algebras of analysis have this property. Examples are discussed to show that (a) neither hermiticity nor ∂ A = Δ (A) can be omitted, and that (b) in case (ii), ∂ A = Δ (A) is not a necessary condition.
Item Type:  Article 

Source:  Copyright of this article belongs to American Mathematical Society. 
Keywords:  Topological Divisor of Zero; Hermitian Banach^{∗}algebra; Orthogonal Basis; Uniform Banach Algebra 
ID Code:  59691 
Deposited On:  07 Sep 2011 05:16 
Last Modified:  18 May 2016 10:10 
Repository Staff Only: item control page