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.

Citation Formats
A. Dosi, “LOCAL OPERATOR ALGEBRAS FRACTIONAL POSITIVITY AND THE QUANTUM MOMENT PROBLEM,” TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 363, no. 2, pp. 801–856, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63574.