Only ‘free’ measures are admissable on 𝐹(𝑆) when the inner product space 𝑆 is incomplete-Reference-Cited by-同舟云学术

Only ‘free’ measures are admissable on 𝐹(𝑆) when the inner product space 𝑆 is incomplete

Published:2007-11-30 Issue:3 Volume:136 Page:919-922
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Buhagiar D.,Chetcuti E.

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 S is a sufficient (and of course, a necessary) condition for S S to be a Hilbert space.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2008-136-03/S0002-9939-07-08982-4/S0002-9939-07-08982-4.pdf

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