A SURVEY ON MULTINORMED VON NEUMANN ALGEBRAS
PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, vol.43, no.1, pp.3-67, 2017 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 43 Issue: 1
- Publication Date: 2017
- Journal Name: PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.3-67
- Middle East Technical University Affiliated: Yes
Abstract
The present paper is devoted to multinormed von Neumann algebras. We pick up basic facts on von Neumann algebras to introduce their locally convex versions. A key construction in this direction is a central topology of a von Neumann algebra. Every multinormed von Neumann algebra can be realized as a local von Neumann algebra on a certain domain in a Hilbert space. It admits the predual (unique up to an isometry), which is an l(1)-normed space. As the main result we describe multinormed L-infinity- algebras which are locally convex analogs of abelian von Neumann algebras.