Gelfand-Mazur algebras. (English) Zbl 0840.46029

Lau, Anthony To-Ming (ed.) et al., Topological vector spaces, algebras and related areas. Proceedings of the international conference, held at McMaster University, Hamilton, Canada during May 2-6, 1994 in honor of Dr. Taqdir Husain on the occasion of his retirement. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 316, 116-129 (1994).
Summary: It is known that all exponentially galbed algebras, all locally pseudoconvex Waelbroeck algebras, all locally \(A\)-pseudoconvex algebras (in particular, all locally \(m\)-pseudoconvex algebras) and all locally pseudoconvex Fréchet algebras are Gel’fand-Mazur algebras. In the present paper, we give several equivalent conditions for a topological algebra to be a Gel’fand-Mazur algebra. The case of non-associative topological algebras is considered separately. Several classes of Jordan Gel’fand-Mazur algebras are presented.
For the entire collection see [Zbl 0817.00016].


46H05 General theory of topological algebras
46H70 Nonassociative topological algebras