A note on transforms of subspaces of Hilbert space
Author: W. E. Longstaff
Journal: Proc. Amer. Math. Soc. 76 (1979), 268-270
MSC: Primary 47B99; Secondary 46C10
MathSciNet review: 537086
Abstract: The transform of a family of (closed linear) subspaces of a Hilbert space H by an invertible (bounded, linear) operator S on H is the family of subspaces . It is shown that the set of projections is closed in the uniform (respectively, strong, weak) operator topology if and only if the set of projections is uniformly (respectively, strongly, weakly) closed. This answers affirmatively a question raised by K. J. Harrison.