Segal extensions and Segal algebras in uniform Banach algebras

Subhash J. Bhatt () and Prakash A. Dabhi ()
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Subhash J. Bhatt: Sardar Patel University
Prakash A. Dabhi: Sardar Patel University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 1, 162-167

Abstract: Abstract Segal extensions, not necessarily injective, of a Banach algebra into a Banach algebra are discussed resulting into answering when do the Gelfand map of a commutative Banach algebra as well as Gelfand-Naimark construction on a, not necessarily commutative, Banach $$*$$ ∗ -algebra give Segal extensions. Analogous to $$C^*$$ C ∗ -Segal algebras arising from Segal extension into $$C^*$$ C ∗ - algebras, uB-Segal algebras arising from Segal extensions into uniform Banach algebras are intrinsically characterized.

Keywords: Banach algebra; Uniform Banach algebra; Segal algebra; Banach $$*$$ ∗ - algebra; $$C^*$$ C ∗ - algebra; $$C^*$$ C ∗ -Segal algebra; Primary 46H05; Secondary 46K05; 46J05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00063-2

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