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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Only `free' measures are admissable on $ F(S)$ when the inner product space $ S$ is incomplete


Authors: D. Buhagiar and E. Chetcuti
Journal: Proc. Amer. Math. Soc. 136 (2008), 919-922
MSC (2000): Primary 46C05, 46C15; Secondary 46L30
Published electronically: November 30, 2007
MathSciNet review: 2361864
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08982-4
PII: S 0002-9939(07)08982-4
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.