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Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

The Mackey-Gleason problem

Author(s): L. J. Bunce; J. D. Maitland Wright
Journal: Bull. Amer. Math. Soc. 26 (1992), 288-293.
MSC (2000): Primary 46L50
MathSciNet review: 1121569
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Abstract | References | Similar articles | Additional information

Abstract: Let A be a von Neumann algebra with no direct summand of Type $ {{\text{I}}_2}$, and let $ \mathcal{P}(A)$ be its lattice of projections. Let X be a Banach space. Let $ m:\mathcal{P}(A) \to X$ be a bounded function such that $ m(p + q) = m(p) + m(q)$ whenever p and q are orthogonal projections. The main theorem states that m has a unique extension to a bounded linear operator from A to X. In particular, each bounded complex-valued finitely additive quantum measure on $ \mathcal{P}(A)$ has a unique extension to a bounded linear functional on A.

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Additional Information:

DOI: 10.1090/S0273-0979-1992-00274-4
PII: S 0273-0979(1992)00274-4
Copyright of article: Copyright 1992, American Mathematical Society




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