A characterization of reflexive spaces of operators |
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Authors: | Janko Bračič Lina Oliveira |
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Institution: | 1.Naravoslovnotehni?ka Fakulteta,University of Ljubljana,Ljubljana,Slovenia;2.Center for Mathematical Analysis, Geometry and Dynamical Systems, and Department of Mathematics, Instituto Superior Técnico,Universidade de Lisboa, Av. Rovisco Pais,Lisboa,Portugal |
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Abstract: | We show that for a linear space of operators M ? B(H1, H2) the following assertions are equivalent. (i) M is reflexive in the sense of Loginov-Shulman. (ii) There exists an order-preserving map Ψ = (ψ1, ψ2) on a bilattice Bil(M) of subspaces determined by M with P ≤ ψ1(P,Q) and Q ≤ ψ2(P,Q) for any pair (P,Q) ∈ Bil(M), and such that an operator T ∈ B(H1, H2) lies in M if and only if ψ2(P,Q)Tψ1(P,Q) = 0 for all (P,Q) ∈ Bil(M). This extends the Erdos-Power type characterization of weakly closed bimodules over a nest algebra to reflexive spaces. |
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