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A quantization procedure based on completely positive maps and Markov operators
We describe -limit sets of completely positive (CP) maps over
finite-dimensional spaces. In such sets and in its corresponding convex hulls,
CP maps present isometric behavior and the states contained in it commute with
each other. Motivated by these facts, we describe a quantization procedure
based on CP maps which are induced by Markov (transfer) operators. Classical
dynamics are described by an action over essentially bounded functions. A
non-expansive linear map, which depends on a choice of a probability measure,
is the centerpiece connecting phenomena over function and matrix spaces
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