Invariant linear manifolds for CSL-algebras and nest algebras

Author:
Alan Hopenwasser

Journal:
Proc. Amer. Math. Soc. **129** (2001), 389-395

MSC (2000):
Primary 47L35

Published electronically:
August 29, 2000

MathSciNet review:
1707148

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Abstract | References | Similar Articles | Additional Information

Every invariant linear manifold for a CSL-algebra, , is a closed subspace if, and only if, each non-zero 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 non-zero 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 non-zero 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/S0002-9939-00-05596-9

Keywords:
Nest algebra,
CSL-algebra,
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