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Maximality of analytic operator algebras
Authors:Baruch Solel
Affiliation:(1) Department of Mathematics and Computer Science, University of Haifa, Mount Carmel, 31999 Haifa, Israel
Abstract:LetM be a σ-finite von Neumann algebra andα be an action ofR onM. LetH (α) be the associated analytic subalgebra; i.e.H (α)={XM: sp(X) [0, ∞]}. We prove that every σ-weakly closed subalgebra ofM that containsH (α) isH (γ) for some actionγ ofR onM. Also we show that (assumingZ(M)∩M α = Ci)H (α) is a maximal σ-weakly closed subalgebra ofM if and only if eitherH (α)={AM: (I−F)xF=0} for some projectionFM, or sp(α)=Γ(α).
Keywords:
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