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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Full subalgebras of Jordan-Banach algebras and algebra norms on $\textrm {JB}^ *$-algebras
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by J. Pérez, L. Rico and A. Rodríguez PDF
Proc. Amer. Math. Soc. 121 (1994), 1133-1143 Request permission

Abstract:

We introduce normed Jordan Q-algebras, namely, normed Jordan algebras in which the set of quasi-invertible elements is open, and we prove that a normed Jordan algebra is a Q-algebra if and only if it is a full subalgebra of its completion. Homomorphisms from normed Jordan Q-algebras onto semisimple Jordan-Banach algebras with minimality of norm topology are continuous. As a consequence, the topology of the norm of a $J{B^ \ast }$-algebra is the smallest normable topology making the product continuous, and $J{B^ \ast }$-algebras have minimality of the norm. Some applications to (associative) ${C^ \ast }$-algebras are also given: (i) the associative normed algebras that are ranges of continuous (resp. contractive) Jordan homomorphisms from ${C^ \ast }$-algebras are bicontinuously (resp. isometrically) isomorphic to ${C^ \ast }$-algebras, and (ii) weakly compact Jordan homomorphisms from ${C^ \ast }$-algebras are of finite rank.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 1133-1143
  • MSC: Primary 46H70; Secondary 17C65, 46L70
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1195486-9
  • MathSciNet review: 1195486