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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
Journal
PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS
Collections
Natural Sciences and Mathematics, Article
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A. Dosi, “A SURVEY ON MULTINORMED VON NEUMANN ALGEBRAS,”
PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS
, pp. 3–67, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63740.