Commutants of reflexive algebras and classification of completely distributive subspace lattices
Authors:
Pengtong Li, Shijie Lu and Jipu Ma
Translated by:
Journal:
Proc. Amer. Math. Soc. 132 (2004), 20052012
MSC (2000):
Primary 47L35, 47L75
Published electronically:
December 31, 2003
MathSciNet review:
2053972
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Abstract: Let be a subspace lattice on a normed space containing a nontrivial comparable element. If commutes with all the operators in , then there exists a scalar such that . Furthermore, we classify the class of completely distributive subspace lattices into subclasses called Type , Type and Type , respectively. It is shown that nontrivial nests or, more generally, completely distributive subspace lattices with a comparable element are Type , and that nontrivial atomic Boolean subspace lattices are Type .
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Additional Information
Pengtong Li
Affiliation:
Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China
Email:
pengtonglee@vip.sina.com
Shijie Lu
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
Address at time of publication:
City College, Zhejiang University, Hangzhou 310015, People’s Republic of China
Email:
lusj@zucc.edu.cn
Jipu Ma
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
DOI:
http://dx.doi.org/10.1090/S0002993903073258
PII:
S 00029939(03)073258
Keywords:
Reflexive algebras,
commutants,
complete distributivity,
comparable elements,
rank one operators
Received by editor(s):
November 19, 2001
Received by editor(s) in revised form:
March 16, 2003
Published electronically:
December 31, 2003
Communicated by:
David R. Larson
Article copyright:
© Copyright 2003
American Mathematical Society
