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A general view of reflexivity


Author: Don Hadwin
Journal: Trans. Amer. Math. Soc. 344 (1994), 325-360
MSC: Primary 47D25; Secondary 46B28, 46L05, 46M20, 47A99, 47D15
DOI: https://doi.org/10.1090/S0002-9947-1994-1239639-4
MathSciNet review: 1239639
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Abstract: Various concepts of reflexivity for an algebra or linear space of operators have been studied by operator theorists and algebraists. This paper contains a very general version of reflexivity based on dual pairs of vector spaces over a Hausdorff field. The special cases include topological, algebraic and approximate reflexivity. In addition general versions of hyperreflexivity and direct integrals are introduced. We prove general versions of many known (and some new) theorems, often with simpler proofs.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1239639-4
Article copyright: © Copyright 1994 American Mathematical Society

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