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Reflexivity for subspace maps and linear spaces of operators. (English) Zbl 0609.47053

The purpose of this paper is to give a systematic account of generalized reflexivity in a new formulation which contains an object analogous to lattices. Many results concerning algebras and lattices are extended to the new situation. This concept of reflexivity has already proved its worth.
The main result is a lifting theorem, and it is applied to Larson’s characterization of reflexivity.
Reviewer: P.E.T.Jørgensen

MSC:

47L05 Linear spaces of operators
47A15 Invariant subspaces of linear operators
47L30 Abstract operator algebras on Hilbert spaces
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