Multinormed W^∗-algebras and unbounded operators

2012/04/03 by Anar Dosi · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Banach Space Theory

paper · pdf · doi:10.1090/s0002-9939-2012-11358-9

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.

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