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