LOCAL OPERATOR ALGEBRAS FRACTIONAL POSITIVITY AND THE QUANTUM MOMENT PROBLEM


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Dosi A.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.363, no.2, pp.801-856, 2011 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 363 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.1090/s0002-9947-2010-05145-1
  • Journal Name: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.801-856
  • Keywords: Local operator algebra, quantum system, quantum moment problem, fractional space, fractional positivity, SPACES

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 *-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.