Mielnik and cantoni transition probabilities

Stanley Gudder

Nicolas Hadjisavvas

Platon C. Deliyannis

An alternative axiomatic system describing the concept of conditioning (or preparation) of states in a quantum logic is proposed and its consequences developed. The main difference between this and the system proposed by Pool is our reliance on Mielnik’s idea of transition probabilities, thereby avoiding some ad hoc hypotheses as well as the theory of Baer *-semigroups.

Robert L. Brooks

Pieter E. Vermaas

Salvatore Guccione, Časlav V. Stanojević

A construction of Mielnik probability spaces of dimension 2 is given in terms of Rubin-Stone functionals, and conversely it is shown that if a certain subset of a real linear space is supplied with 2 dimensional Mielnik probability space structure then the space becomes a Rubin-Stone space (in final analysis, a generalized inner product space).Analogous results are given for generalized inner product spaces in the sense of Nagumo.