Gelfand–Mazur Theorems in normed algebras: A survey

Autor:	S. H. Kulkarni, S.J. Bhatt
Rok vydání:	2018
Předmět:	Discrete mathematics Normed algebra Pure mathematics General Mathematics Clifford algebra symbols.namesake Classification of Clifford algebras Gelfand–Naimark theorem symbols Division algebra Algebra representation Frobenius theorem (real division algebras) Banach–Mazur theorem Mathematics
Zdroj:	Expositiones Mathematicae. 36:166-177
ISSN:	0723-0869
DOI:	10.1016/j.exmath.2017.08.004
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::94b51c6dbbdff827fc447d9021d580ac https://doi.org/10.1016/j.exmath.2017.08.004 Zobrazit plný text záznamu Full Text from ScienceDirect