Skip Navigation

Journal of the London Mathematical Society 1988 s2-37(3):499-508; doi:10.1112/jlms/s2-37.3.499
© 1988 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Longstaff, W. E.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© Oxford University Press

On Lattices Whose Every Realization on Hilbert Space is Reflexive

W. E. Longstaff

Department of Mathematics, The University of Western Australia Nedlands, Western Australia 6009

Received 13 April 1987.

Let L be an abstract complete lattice. Call a subspace lattice L on a complex Hilbert space H a realization of L on H if L is lattice-isomorphic to L. The author has previously observed that if L is completely distributive, then every realization of it is reflexive. Here the converse is proved under the additional assumption that L has a realization on a finite-dimensional space. This is done by showing that every non-distributive subspace lattice on a finite-dimensional space has a non-reflexive realization on the same space.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.