A constructive proof of Gleason's theorem
type: Item
instance of: scholarly article
title: A constructive proof of Gleason's theorem
zbMATH Open document ID: 0928.46040
author: Fred Richman
author: Douglas Bridges
published in: Journal of Functional Analysis
publication date: 2000-01-09T00:00:00Z
review text: Gleason's theorem states that any totally additive measure on the closed subspaces of a Hilbert space of dimension greater than two is given by a positive operator of trace class. \textit{R. Cooke}, \textit{M. Keane} and \textit{W. Moran} [Math. Proc. Camb. Philos. Soc. 98, 117-128 (1985; Zbl 0575.46051)] gave a proof that is elementary in the sense that unlike the original proof it doesn't appeal to the theory of representations of the orthogonal group. However, this elementary proof was nonconstructive. Therefore, the authors follow the general outline of Gleason's proof, modify some arguments of Cooke, Keane and Moran and give a constructive proof of Gleason's theorem.
Mathematics Subject Classification ID: 46L51
zbMATH DE Number: 1274801
zbMATH Keywords: measure on closed subspaces
zbMATH Keywords: trace class operator
zbMATH Keywords: representations of the orthogonal group
zbMATH Keywords: constructive proof of Gleason's theorem
reviewed by: Sh. A. Ayupov
MaRDI profile type: Publication
OpenAlex ID: W2053340053
Wikidata QID: Q57380996
cites work: A constructive formulation of Gleason's theorem
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cites work: Q3245484
cites work: Gleason's theorem is not constructively provable
cites work: Q3866110
cites work: Diagonalization of continuous matrices as a representation of intuitionistic reals
DOI: 10.1006/JFAN.1998.3372
description: scientific article; zbMATH DE number 1274801