Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


Every invariant linear manifold for a CSL-algebra, $\operatorname{Alg} \mathcal{L}$, is a closed subspace if, and only if, each non-zero projection in $\mathcal{L}$ is generated by finitely many atoms associated with the projection lattice. When $\mathcal{L}$is a nest, this condition is equivalent to the condition that every non-zero projection in $\mathcal{L}$ has an immediate predecessor ( $\mathcal{L}^{\perp}$ 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47L35

Retrieve articles in all journals with MSC (2000): 47L35

Additional Information

Alan Hopenwasser
Affiliation: Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487

PII: S 0002-9939(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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia