MULTINORMED W*-ALGEBRAS AND UNBOUNDED OPERATORS


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Dosi A.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.140, no.12, pp.4187-4202, 2012 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 140 Issue: 12
  • Publication Date: 2012
  • Doi Number: 10.1090/s0002-9939-2012-11358-9
  • Journal Name: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.4187-4202
  • Keywords: Multinormed W*-algebra, unbounded operators, central topology, l(1)-normed space

Abstract

In this paper we investigate multinormed W*-algebras in terms of the central topologies of W*-algebras. The main result asserts that each multinormed W*-algebra can be realized as a local von Neumann algebra on a certain domain in a Hilbert space. Moreover, it admits the predual (unique up to an isometry), which is the l(1)-normed space. In the normed case the assertion is reduced to the known Sakai theorem.