Only ‘free’ measures are admissable on $F(S)$ when the inner product space $S$ is incomplete
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- by D. Buhagiar and E. Chetcuti PDF
- Proc. Amer. Math. Soc. 136 (2008), 919-922 Request permission
Abstract:
Using elementary arguments and without having to recall the Gleason Theorem, we prove that the existence of a nonsingular measure on the lattice of orthogonally closed subspaces of an inner product space $S$ is a sufficient (and of course, a necessary) condition for $S$ to be a Hilbert space.References
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Additional Information
- D. Buhagiar
- Affiliation: Department of Mathematics, Faculty of Science, University of Malta, Msida MSD.06, Malta
- Email: david.buhagiar@um.edu.mt
- E. Chetcuti
- Affiliation: Department of Mathematics, Junior College, University of Malta, Msida MSD.06, Malta
- Email: emanuel.chetcuti@um.edu.mt
- Received by editor(s): May 24, 2006
- Received by editor(s) in revised form: October 11, 2006
- Published electronically: November 30, 2007
- Communicated by: David Preiss
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 919-922
- MSC (2000): Primary 46C05, 46C15; Secondary 46L30
- DOI: https://doi.org/10.1090/S0002-9939-07-08982-4
- MathSciNet review: 2361864