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

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Completely $ 1$-complemented subspaces of Schatten spaces


Authors: Christian Le Merdy, Éric Ricard and Jean Roydor
Journal: Trans. Amer. Math. Soc. 361 (2009), 849-887
MSC (2000): Primary 46L07, 46L89, 17C65
Published electronically: August 14, 2008
MathSciNet review: 2452827
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the Schatten spaces $ S^p$ in the framework of operator space theory and for any $ 1\leq p\not=2<\infty$, we characterize the completely $ 1$-complemented subspaces of $ S^p$. They turn out to be the direct sums of spaces of the form $ S^p(H,K)$, where $ H,K$ are Hilbert spaces. This result is related to some previous work of Arazy and Friedman giving a description of all $ 1$-complemented subspaces of $ S^p$ in terms of the Cartan factors of types 1-4. We use operator space structures on these Cartan factors regarded as subspaces of appropriate noncommutative $ L^p$-spaces. Also we show that for any $ n\geq 2$, there is a triple isomorphism on some Cartan factor of type 4 and of dimension $ 2n$ which is not completely isometric, and we investigate $ L^p$-versions of such isomorphisms.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46L07, 46L89, 17C65

Retrieve articles in all journals with MSC (2000): 46L07, 46L89, 17C65


Additional Information

Christian Le Merdy
Affiliation: Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France
Email: clemerdy@univ-fcomte.fr

Éric Ricard
Affiliation: Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France
Email: eric.ricard@univ-fcomte.fr

Jean Roydor
Affiliation: Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France
Email: jean.roydor@univ-fcomte.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04594-7
PII: S 0002-9947(08)04594-7
Received by editor(s): March 27, 2007
Published electronically: August 14, 2008
Article copyright: © Copyright 2008 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