A Kaplansky theorem for \(JB^*\)-algebras
type: Item
instance of: scholarly article
title: A Kaplansky theorem for \(JB^*\)-algebras
zbMATH Open document ID: 0932.46062
published in: Rocky Mountain Journal of Mathematics
publication date: 2000-03-08T00:00:00Z
full work available at URL: cont28-3.html
review text: In 1949, Irving Kaplansky proved that any algebra norm on \(C(X)\) dominates the standard uniform norm. This result was extended to noncommutative \(C^*\)-algebras (modulo some constant) by S. B. Cleveland. This result was extended, in 1994, to \(JB^*\)-algebras by J. Perez, L. Rico and A. Rodriguez Palacios. The two authors of this paper give a slightly different proof of this last result, essentially based on Cleveland's ideas. I only mention that the proof of Theorem 4 is not complete, because every element of the separating space could be quasinilpotent. But then, having noticed that it is easy to finish.
reviewed by: Bernard Aupetit
Mathematics Subject Classification ID: 46L70
zbMATH DE Number: 1309861
zbMATH Keywords: Kaplansky theorem
zbMATH Keywords: \(JB^*\)-algebras
author: Shirin Hejazian
author: Assadollah Niknam
MaRDI profile type: Publication
OpenAlex ID: W2073421594
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DOI: 10.1216/RMJM/1181071749
description: scientific article; zbMATH DE number 1309861