Invariant linear manifolds for CSLalgebras and nest algebras
Author:
Alan Hopenwasser
Journal:
Proc. Amer. Math. Soc. 129 (2001), 389395
MSC (2000):
Primary 47L35
Published electronically:
August 29, 2000
MathSciNet review:
1707148
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Abstract: Every invariant linear manifold for a CSLalgebra, , is a closed subspace if, and only if, each nonzero projection in is generated by finitely many atoms associated with the projection lattice. When is a nest, this condition is equivalent to the condition that every nonzero projection in has an immediate predecessor ( is well ordered). The invariant linear manifolds of a nest algebra are totally ordered by inclusion if, and only if, every nonzero projection in the nest has an immediate predecessor.
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Additional Information
Alan Hopenwasser
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487
Email:
ahopenwa@euler.math.ua.edu
DOI:
http://dx.doi.org/10.1090/S0002993900055969
PII:
S 00029939(00)055969
Keywords:
Nest algebra,
CSLalgebra,
invariant subspace,
invariant linear manifold
Received by editor(s):
June 15, 1998
Received by editor(s) in revised form:
April 8, 1999
Published electronically:
August 29, 2000
Additional Notes:
The author would like to thank Ken Davidson for drawing his attention to the references regarding operator ranges.
Communicated by:
David R. Larson
Article copyright:
© Copyright 2000 American Mathematical Society
