Skip Navigation



The Quarterly Journal of Mathematics Advance Access published online on January 31, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham053
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 Bresar, M.
Right arrow Articles by Shulman, V. S.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2007. Published by Oxford University Press. All rights reserved For permissions, please email: journals.permissions@oxfordjournals.org

WHEN JORDAN SUBMODULES ARE BIMODULES

Matej Bresar{dagger}

Department of Mathematics and Computer Science, FNM, University of Maribor, Koroska cesta 160, 2000 Maribor, Slovenia

Edward Kissin {ddagger}

Department of Computing, Communications Technology and Mathematics, London Metropolitan University, 166-220 Holloway Road, London N7 8DB, UK

Victor S. Shulman §

Department of Mathematics, Vologda State Technical University, Vologda, Russia

{dagger} Corresponding author. E-mail: bresar{at}uni-mb.si

Received 23 March 2007; revised 22 October 2007
  Abstract

Let A be an algebra and let X be an A-bimodule. We call a linear subspace Y of X a Jordan A-submodule of X if Ay + yA isin Y for all A isin A and y isin Y (if X = A, then this coincides with the classical concept of a Jordan ideal). When is a Jordan A-submodule a submodule? We give a thorough analysis of this question in both algebraic and analytic context. In the first part of the paper, we consider general algebras and general Banach algebras. In the second part, we treat some more specific topics, such as symmetrically normed Jordan A-submodules. Some of our results are of interest also in the classical situation; in particular, we show that there exist C*-algebras having Jordan ideals that are not ideals.

{ddagger} E-mail: e.kissin{at}londonmet.ac.uk

§ E-mail: shulman-v{at}yahoo.com


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.