3 years ago

Gelfand–Mazur Theorems in normed algebras: A survey

S.j. Bhatt, S.h. Kulkarni

Publication date: June 2018

Source: Expositiones Mathematicae, Volume 36, Issue 2

Author(s): S.J. Bhatt, S.H. Kulkarni

Abstract

The Gelfand–Mazur Theorem, a very basic theorem in the theory of Banach algebras states that: (Real version) Every real normed division algebra is isomorphic to the algebra of all real numbers R, the complex numbers C or the quaternions H; (Complex version) Every complex normed division algebra is isometrically isomorphic to C. This theorem has undergone a large number of generalizations. We present a survey of these generalizations and also discuss some closely related unsettled issues.

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