Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

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
MathSciNet review: 1121569
Full-text PDF

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 46L50

Retrieve articles in all journals with MSC (2000): 46L50


Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1992-00274-4
PII: S 0273-0979(1992)00274-4
Article copyright: © Copyright 1992 American Mathematical Society