Research Highlights

Segal extensions and Segal algebras in uniform Banach algebras

Authors :- Subhash J. Bhatt & Prakash A. Dabhi

Publication :- Indian Journal of Pure and Applied Mathematics volume 52, pages162–167 (2021).

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∗-Segal algebras arising from Segal extension into C∗- algebras, uB-Segal algebras arising from Segal extensions into uniform Banach algebras are intrinsically characterized.