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LOCAL OPERATOR ALGEBRAS FRACTIONAL POSITIVITY AND THE QUANTUM MOMENT PROBLEM

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2011-02-01
Dosi, Anar
In the present paper we introduce quantum measures as a concept of quantum functional analysis and develop the fractional space technique in the quantum (or local operator) space framework. We prove that each local operator algebra (or quantum *-algebra) has a fractional space realization. This approach allows us to formulate and prove a noncommutative Albrecht-Vasilescu extension theorem, which in turn solves the quantum moment problem.