The Mackey-Gleason problem

Authors:
L. J. Bunce and J. D. Maitland Wright

Journal:
Bull. Amer. Math. Soc. **26** (1992), 288-293

MSC (2000):
Primary 46L50

DOI:
https://doi.org/10.1090/S0273-0979-1992-00274-4

MathSciNet review:
1121569

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Abstract: Let *A* be a von Neumann algebra with no direct summand of Type , and let be its lattice of projections. Let *X* be a Banach space. Let be a bounded function such that 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 has a unique extension to a bounded linear functional on *A*.

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DOI:
https://doi.org/10.1090/S0273-0979-1992-00274-4

Article copyright:
© Copyright 1992
American Mathematical Society