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)

 

Multinormed $ W^{\ast}$-algebras and unbounded operators


Author: Anar Dosi
Journal: Proc. Amer. Math. Soc. 140 (2012), 4187-4202
MSC (2010): Primary 46K10; Secondary 47L25, 47L60
Published electronically: April 3, 2012
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we investigate multinormed $ W^{\ast }$-algebras in terms of the central topologies of $ W^{\ast }$-algebras. The main result asserts that each multinormed $ W^{\ast }$-algebra can be realized as a local von Neumann algebra on a certain domain in a Hilbert space. Moreover, it admits the predual (unique up to an isometry), which is the $ \ell _{1}$-normed space. In the normed case the assertion is reduced to the known Sakai theorem.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46K10, 47L25, 47L60

Retrieve articles in all journals with MSC (2010): 46K10, 47L25, 47L60


Additional Information

Anar Dosi
Affiliation: Middle East Technical University Northern Cyprus Campus, Guzelyurt, KKTC, Mersin 10, Turkey
Email: dosiev@yahoo.com, dosiev@metu.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11358-9
PII: S 0002-9939(2012)11358-9
Keywords: Multinormed $W^*$-algebra, unbounded operators, central topology, $\ell_1$-normed space
Received by editor(s): March 15, 2010
Received by editor(s) in revised form: May 18, 2011
Published electronically: April 3, 2012
Additional Notes: The author thanks the institution TUBITAK for encouraging research papers in Turkey
Communicated by: Marius Junge
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.