Subspace maps of operators on Hilbert space

Author:
W. E. Longstaff

Journal:
Proc. Amer. Math. Soc. **84** (1982), 195-201

MSC:
Primary 47A05; Secondary 47A10

DOI:
https://doi.org/10.1090/S0002-9939-1982-0637168-7

MathSciNet review:
637168

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Abstract: An operator acting on a Hilbert space gives rise to a map on the set of subspaces of given by , where denotes norm closure. This map is called the subspace map of . By identifying subspaces with projections in the usual way it is shown that for , is uniformly (respectively, strongly) continuous if and only if the approximate point spectrum of does not contain 0. In this case it is proved that preserves the property of being uniformly (respectively, strongly, weakly) closed and its effect on reflexivity is described.

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DOI:
https://doi.org/10.1090/S0002-9939-1982-0637168-7

Article copyright:
© Copyright 1982
American Mathematical Society