Local operator algebras, fractional positivity and the quantum moment problem

Dosi, Anar

doi:10.1090/S0002-9947-2010-05145-1

Local operator algebras, fractional positivity and the quantum moment problem
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Trans. Amer. Math. Soc. 363 (2011), 801-856 Request permission

Abstract:

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 $\ast$-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.

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