A note on transforms of subspaces of Hilbert space
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- by W. E. Longstaff PDF
- Proc. Amer. Math. Soc. 76 (1979), 268-270 Request permission
Abstract:
The transform of a family $\mathcal {F}$ of (closed linear) subspaces of a Hilbert space H by an invertible (bounded, linear) operator S on H is the family of subspaces $\{ SM:M \in \mathcal {F}\}$. It is shown that the set of projections $\{ {P_{SM}}:M \in \mathcal {F}\}$ is closed in the uniform (respectively, strong, weak) operator topology if and only if the set of projections $\{ {P_M}:M \in \mathcal {F}\}$ is uniformly (respectively, strongly, weakly) closed. This answers affirmatively a question raised by K. J. Harrison.References
- K. J. Harrison, Transitive atomic lattices of subspaces, Indiana Univ. Math. J. 21 (1971/72), 621–642. MR 291850, DOI 10.1512/iumj.1972.21.21049
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 268-270
- MSC: Primary 47B99; Secondary 46C10
- DOI: https://doi.org/10.1090/S0002-9939-1979-0537086-9
- MathSciNet review: 537086