A SURVEY ON MULTINORMED VON NEUMANN ALGEBRAS

Date

2017-01-01

Author

Dosi, Anar

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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.

Subject Keywords

Multinormed Von Neumann Algebra, Unbounded Operators, Central Topology, L(1)-Normed Space

URI

https://hdl.handle.net/11511/63740

Collections

Natural Sciences and Mathematics, Article