Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A Cartan theorem for Banach algebras
HTML articles powered by AMS MathViewer

by Thomas Ransford PDF
Proc. Amer. Math. Soc. 124 (1996), 243-247 Request permission

Abstract:

Let $A$ be a semisimple Banach algebra, and let $\Omega _A$ be its spectral unit ball. We show that every holomorphic map $G\colon \Omega _A\to \Omega _A$ satisfying $G(0)=0$ and $G’(0)=I$ fixes those elements of $\Omega _A$ which belong to the centre of $A$, but not necessarily any others. Using this, we deduce that the automorphisms of $\Omega _A$ all leave the centre invariant. As a further application, we give a new proof of Nagasawa’s generalization of the Banach-Stone theorem.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46Hxx, 32Hxx
  • Retrieve articles in all journals with MSC (1991): 46Hxx, 32Hxx
Additional Information
  • Thomas Ransford
  • Affiliation: Département de Mathématiques et de Statistique, Université Laval, Québec (QC), Canada G1K 7P4
  • MR Author ID: 204108
  • Email: ransford@mat.ulaval.ca
  • Received by editor(s): August 24, 1994
  • Additional Notes: The author was supported by grants from NSERC and FCAR
  • Communicated by: Theodore Gamelin
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 243-247
  • MSC (1991): Primary 46Hxx; Secondary 32Hxx
  • DOI: https://doi.org/10.1090/S0002-9939-96-03197-8
  • MathSciNet review: 1307559