Weakly closed Lie modules of nest algebras

2015/12/10 by Lina Oliveira, Oliveira, Lina, Miguel Santos +1
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1512.03408

arxiv created 2015/12/10 · arxiv updated 2015/12/11

Abstract

Let T(N) be a nest algebra of operators on Hilbert space and let L be a weakly closed Lie T(N)-module. We construct explicitly the largest possible weakly closed T(N)-bimodule J(L) and a weakly closed T(N)-bimodule K(L) such that J(L)⊆ L ⊆ K(L) +D_K(L), [K(L), T(N)]⊆ L and D_K(L) is a von Neumann subalgebra of the diagonal T(N)∩ T(N)^*.

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• Finite rank operators in Lie ideals of nest algebras
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• Bimodules of Banach space nest algebras
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