Algebraic isomorphisms and subspace lattices
Authors:
Jiankui Li and Oreste Panaia
Journal:
Proc. Amer. Math. Soc. 133 (2005), 25772587
MSC (2000):
Primary 47L10
Published electronically:
April 15, 2005
MathSciNet review:
2146201
Fulltext PDF Free Access
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Abstract: The class of lattices was originally defined in the second author's thesis and subsequently by Longstaff, Nation, and Panaia. A subspace lattice on a Banach space which is also a lattice is called a subspace lattice, abbreviated JSL. It is demonstrated that every single element of has rank at most one. It is also shown that has the strong finite rank decomposability property. Let and be subspace lattices that are also JSL's on the Banach spaces and , respectively. The two properties just referred to, when combined, show that every algebraic isomorphism between and preserves rank. Finally we prove that every algebraic isomorphism between and is quasispatial.
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Additional Information
Jiankui Li
Affiliation:
Department of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email:
jli@math.uwaterloo.ca
Oreste Panaia
Affiliation:
School of Mathematics, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia
Email:
oreste@maths.uwa.edu.au
DOI:
http://dx.doi.org/10.1090/S0002993905075817
PII:
S 00029939(05)075817
Keywords:
Algebraic isomorphism,
rankone operator,
single element
Received by editor(s):
February 4, 2002
Received by editor(s) in revised form:
April 17, 2003
Published electronically:
April 15, 2005
Communicated by:
David R. Larson
Article copyright:
© Copyright 2005 American Mathematical Society
