A SURVEY ON MULTINORMED VON NEUMANN ALGEBRAS


Dosi A.

PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, cilt.43, sa.1, ss.3-67, 2017 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 43 Konu: 1
  • Basım Tarihi: 2017
  • Dergi Adı: PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS
  • Sayfa Sayıları: ss.3-67

Özet

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.