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.


Zero product preserving maps of operator-valued functions
HTML articles powered by AMS MathViewer

by Wen-Fong Ke, Bing-Ren Li and Ngai-Ching Wong PDF
Proc. Amer. Math. Soc. 132 (2004), 1979-1985 Request permission


Let $X,Y$ be locally compact Hausdorff spaces and ${\mathcal M}$, ${\mathcal N}$ be Banach algebras. Let $\theta : C_0(X,{\mathcal M}) \to C_0(Y, {\mathcal N})$ be a zero product preserving bounded linear map with dense range. We show that $\theta$ is given by a continuous field of algebra homomorphisms from ${\mathcal M}$ into ${\mathcal N}$ if ${\mathcal N}$ is irreducible. As corollaries, such a surjective $\theta$ arises from an algebra homomorphism, provided that ${\mathcal M}$ is a $W^*$-algebra and ${\mathcal N}$ is a semi-simple Banach algebra, or both ${\mathcal M}$ and ${\mathcal N}$ are $C^*$-algebras.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46E40, 47B33
  • Retrieve articles in all journals with MSC (2000): 46E40, 47B33
Additional Information
  • Wen-Fong Ke
  • Affiliation: Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan
  • Email:
  • Bing-Ren Li
  • Affiliation: Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China
  • Email:
  • Ngai-Ching Wong
  • Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
  • Email:
  • Received by editor(s): July 25, 2002
  • Received by editor(s) in revised form: March 7, 2003
  • Published electronically: December 15, 2003
  • Communicated by: David R. Larson
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1979-1985
  • MSC (2000): Primary 46E40, 47B33
  • DOI:
  • MathSciNet review: 2053969