Communications in Mathematical Physics

, Volume 98, Issue 2, pp 187–202 | Cite as

Quantum measures and states on Jordan algebras

  • L. J. Bunce
  • J. D. Maitland Wright


A problem of Mackey for von Neumann algebras has been settled by the conjunction of the early work of Gleason and the recent advances of Christensen and Yeadon. We show that Mackey's conjecture holds in much greater generality. LetA be a JBW-algebra and letL be the lattice of all projections inA. A quantum measure onL is a countably additive map,m, fromL into the real numbers. Our results imply thatm always has a unique extension to a bounded linear functional onA, provided thatA has no TypeI2 direct summand.


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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • L. J. Bunce
    • 1
  • J. D. Maitland Wright
    • 1
  1. 1.Department of MathematicsReading UniversityReadingEngland

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