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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Local operator algebras, fractional positivity and the quantum moment problem


Author: Anar Dosi
Journal: Trans. Amer. Math. Soc. 363 (2011), 801-856
MSC (2000): Primary 47L60; Secondary 47L25, 46L07, 46G12
Published electronically: September 30, 2010
MathSciNet review: 2728586
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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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Additional Information

Anar Dosi
Affiliation: Department of Mathematics, Middle East Technical University, Northern Cyprus Campus, Guzelyurt, KKTC via Mersin 10, Turkey
Email: dosiev@yahoo.com, dosiev@metu.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05145-1
PII: S 0002-9947(2010)05145-1
Keywords: Local operator algebra, quantum system, quantum moment problem, fractional space, fractional positivity
Received by editor(s): November 11, 2008
Received by editor(s) in revised form: April 1, 2009
Published electronically: September 30, 2010
Article copyright: © Copyright 2010 American Mathematical Society