A SURVEY ON MULTINORMED VON NEUMANN ALGEBRAS

2017-01-01
Dosi, Anar
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.

Citation Formats
A. Dosi, “A SURVEY ON MULTINORMED VON NEUMANN ALGEBRAS,” PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, vol. 43, no. 1, pp. 3–67, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63740.