Multinormed 𝑊*-algebras and unbounded operators

Dosi, Anar

doi:10.1090/S0002-9939-2012-11358-9

Multinormed $W^{\ast }$-algebras and unbounded operators
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Proc. Amer. Math. Soc. 140 (2012), 4187-4202 Request permission

Abstract:

In this paper we investigate multinormed $W^{\ast }$-algebras in terms of the central topologies of $W^{\ast }$-algebras. The main result asserts that each multinormed $W^{\ast }$-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 $\ell _{1}$-normed space. In the normed case the assertion is reduced to the known Sakai theorem.

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