科研之友
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摘要
We show that for a linear space of operators M subset of B(H-1, H-2) the following assertions are equivalent. (i) M is reflexive in the sense of Loginov-Shulman. (ii) There exists an order-preserving map Psi = (psi(1), psi(2)) on a bilattice Bil(M) of subspaces determined by M with P <= psi(1)(P,Q) and Q <= psi(2)(P,Q) for any pair (P,Q) is an element of Bil(M), and such that an operator T is an element of B(H-1, H-2) lies in M if and only if psi(2)(P,Q)T psi(1)(P,Q) = 0 for all (P,Q) is an element of Bil(M). This extends the Erdos-Power type characterization of weakly closed bimodules over a nest algebra to reflexive spaces.
- 出版日期2018-3
