Zero product preserving maps of operator-valued functions

Authors:
Wen-Fong Ke, Bing-Ren Li and Ngai-Ching Wong

Translated by:

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1979-1985

MSC (2000):
Primary 46E40, 47B33

DOI:
https://doi.org/10.1090/S0002-9939-03-07321-0

Published electronically:
December 15, 2003

MathSciNet review:
2053969

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be locally compact Hausdorff spaces and , be Banach algebras. Let be a zero product preserving bounded linear map with dense range. We show that is given by a continuous field of algebra homomorphisms from into if is irreducible. As corollaries, such a surjective arises from an algebra homomorphism, provided that is a -algebra and is a semi-simple Banach algebra, or both and are -algebras.

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Additional Information

**Wen-Fong Ke**

Affiliation:
Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan

Email:
wfke@mail.ncku.edu.tw

**Bing-Ren Li**

Affiliation:
Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China

Email:
brli@mail2.math.ac.cn

**Ngai-Ching Wong**

Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan

Email:
wong@math.nsysu.edu.tw

DOI:
https://doi.org/10.1090/S0002-9939-03-07321-0

Keywords:
Zero product preserving maps,
Banach algebra homomorphisms

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

Article copyright:
© Copyright 2003
American Mathematical Society