Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A description of Hilbert $\mathbf{\mathit{C}^*}$-modules in which all closed submodules are orthogonally closed

Author: Jürgen Schweizer
Journal: Proc. Amer. Math. Soc. 127 (1999), 2123-2125
MSC (1991): Primary 46L05
Published electronically: March 17, 1999
MathSciNet review: 1646207
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $A$, $B$ be $C^*$-algebras and $E$ a full Hilbert $A$-$B$-bimodule such that every closed right submodule $E_{0}\subseteq E$ is orthogonally closed, i.e., $E_{0}=(E_{0}^{\perp })^{\perp }$. Then there are families of Hilbert spaces $\{\mathcal{H}_{i}\}$, $\{\mathcal{V}_{i}\}$ such that $A$ and $B$ are isomorphic to $c_{0}$-direct sums $\sum \!\mathcal{K}(\mathcal{V}_{i})$, resp. $\sum \!\mathcal{K}(\mathcal{H}_{i})$, and $E$ is isomorphic to the outer direct sum $\sum _{\!0}\mathcal{K}(\mathcal{H}_{i},\mathcal{V}_{i})$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L05

Retrieve articles in all journals with MSC (1991): 46L05

Additional Information

Jürgen Schweizer
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany

PII: S 0002-9939(99)05219-3
Keywords: Hilbert $C^*$-modules, complemented submodules
Received by editor(s): October 23, 1997
Published electronically: March 17, 1999
Additional Notes: The results of this paper are part of the author’s doctoral dissertation at the University of Tübingen, which was completed before we received the preprint \cite{5} by Magajna.
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society