Skip Navigation


Proceedings of the London Mathematical Society Advance Access originally published online on November 4, 2008
Proceedings of the London Mathematical Society 2009 98(3):652-678; doi:10.1112/plms/pdn048
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
98/3/652    most recent
pdn048v1
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 Davidson, K. R.
Right arrow Articles by Ji, Y. Q.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008 London Mathematical Society

Topological stable rank of nest algebras

Kenneth R. Davidson

Pure Mathematics Department
University of Waterloo
Waterloo
Ontario
Canada N2L 3G1

You Qing Ji

Mathematics Department
Jilin University
Changchun 130012
PR China
jiyq@jlu.edu.cn

Received 13 March 2008. Revision received 5 September 2008.

We establish a general result about extending a right invertible row over a Banach algebra to an invertible matrix. This is applied to the computation of right topological stable rank of a split exact sequence. We also introduce a quantitative measure of stable rank. These results are applied to compute the right (left) topological stable rank for all nest algebras. This value is either 2 or infinity, and rtsr (T(N)) = 2 occurs only when N is of ordinal type less than {omega}2 and the dimensions of the atoms grows sufficiently quickly. We introduce general results on ‘partial matrix algebras’ over a Banach algebra. This is used to obtain an inequality akin to Rieffel's formula for matrix algebras over a Banach algebra. This is used to give further insight into the nest case.

2000 Mathematics Subject Classification 47A35, 47L75, 19B10.

The first author was partially supported by an NSERC grant. The second author was partially supported by RFDP(20050183002), NCET and the China Scholarship Council.


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.