A Constructive Proof of Gleason’s Theorem (1999)
by
Fred Richman
,
Douglas Bridges
| Venue: | J. Func. Anal |
| Citations: | 11 - 2 self |
BibTeX
@ARTICLE{Richman99aconstructive,
author = {Fred Richman and Douglas Bridges},
title = {A Constructive Proof of Gleason’s Theorem},
journal = {J. Func. Anal},
year = {1999},
pages = {287--312}
}
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Abstract
Gleason's theorem states that any totally additive measure on the closed subspaces, or projections, of a Hilbert space of dimension greater than two is given by a positive operator of trace class. In this paper we give a constructive proof of that theorem. A measure on the projections of a real or complex Hilbert space assigns to
Citations
| 139 | Measures on the closed subspaces of a Hilbert space - Gleason - 1957 |
| 14 | An Elementay Proof of Gleason’s Theorem - Cooke, M, et al. - 1984 |
| 14 | On inner products in linear, metric spaces - Jordan, Neumann - 1935 |
| 8 | A constructive look at positive linear functionals on L(H - Bridges - 1981 |
| 7 | Gleason’ s Theorem Is Not Constructively Provable - Hellman - 1993 |
| 3 | A constructive formulation of Gleason’s theorem - Billinge - 1997 |
| 1 | Alan (ed.) The logico-algebraic approach to quantum mechanics - Hooker - 1975 |
| 1 | Diagonalization of continuous matrices as a representation of intuitionistic reals - Andre |
