A BanachStone theorem for Riesz isomorphisms of Banach lattices
Authors:
Jin Xi Chen, Zi Li Chen and NgaiChing Wong
Journal:
Proc. Amer. Math. Soc. 136 (2008), 38693874
MSC (2000):
Primary 46E40; Secondary 46B42, 47B65
Published electronically:
June 24, 2008
MathSciNet review:
2425726
Fulltext PDF Free Access
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Abstract: Let and be compact Hausdorff spaces, and , be Banach lattices. Let denote the Banach lattice of all continuous valued functions on equipped with the pointwise ordering and the sup norm. We prove that if there exists a Riesz isomorphism such that is nonvanishing on if and only if is nonvanishing on , then is homeomorphic to , and is Riesz isomorphic to . In this case, can be written as a weighted composition operator: , where is a homeomorphism from onto , and is a Riesz isomorphism from onto for every in . This generalizes some known results obtained recently.
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Additional Information
Jin Xi Chen
Affiliation:
Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China
Email:
jinxichen@home.swjtu.edu.cn
Zi Li Chen
Affiliation:
Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China
Email:
zlchen@home.swjtu.edu.cn
NgaiChing Wong
Affiliation:
Department of Applied Mathematics, National Sun Yatsen University, Kaohsiung 80424, Taiwan
Email:
wong@math.nsysu.edu.tw
DOI:
http://dx.doi.org/10.1090/S0002993908095828
PII:
S 00029939(08)095828
Keywords:
Banach lattice,
BanachStone theorem,
Riesz isomorphism,
weighted composition operator
Received by editor(s):
June 1, 2007
Published electronically:
June 24, 2008
Communicated by:
N. TomczakJaegermann
Article copyright:
© Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
