Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895552 | Expositiones Mathematicae | 2018 | 12 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
S.J. Bhatt, S.H. Kulkarni,