Czechoslovak Mathematical Journal

, Volume 68, Issue 1, pp 257–266 | Cite as

A characterization of reflexive spaces of operators

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Abstract

We show that for a linear space of operators MB(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 TB(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.

Keywords

reflexive space of operators order-preserving map 

MSC 2010

47A15 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Naravoslovnotehniška FakultetaUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Center for Mathematical Analysis, Geometry and Dynamical Systems, and Department of Mathematics, Instituto Superior TécnicoUniversidade de Lisboa, Av. Rovisco PaisLisboaPortugal

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