Abstract:
Arising from investigations of decoherence functionals in the “histories” approach to quantum mechanics, the following result is given by the methods of [14]. Let A 1 and A 2 be von Neumann algebras without Type I 2 direct summands and let P(E j ), (j=1,2) be their lattices of projections. Let m\colon; P(A 1)×(P(A 2)→ℂ be a bounded quantum bi-measure. Then there is a unique bounded bilinear functional M on A 1×A 2 which extends m. In this note we use a different approach to establish a generalisation of this result to k-fold, vector valued, quantum multi-measures. This tool is needed for further investigations of decoherence functionals in quantum theory.
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Received: 10 April 1998 / Accepted: 17 April 1998
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Rudolph, O., Maitland Wright, J. The Multi-form Generalised Gleason Theorem. Comm Math Phys 198, 705–709 (1998). https://doi.org/10.1007/s002200050491
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DOI: https://doi.org/10.1007/s002200050491