Implementation of comparative probability by normal states. Infinite dimensional case |
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| Authors: | Simba A Mutangadura |
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| Institution: | (1) Present address: Department of Physics, University of Zimbabwe, Mt. Pleasant, Box M.P. 167, Harare, Zimbabwe;(2) International Centre for Theoretical Physics, Trieste, Italy |
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| Abstract: | Let  be an infinite dimensional Hilbert space and  () the set of all (orthogonal) projections on . A comparative probability on () is a linear preorder  on () such thatOP1,1 O and such that ifP┴R,Q┴R, thenPQ P+RQ+R for allP, Q, R in (). We give a sufficient and necessary condition for to be implemented in a canonical way by a normal state onB(), the bounded linear operators on . |
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