PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.140, no.12, pp.4187-4202, 2012 (Peer-Reviewed Journal)
Article / Article
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
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Multinormed W*-algebra, unbounded operators, central topology, l(1)-normed space
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.