LOCAL OPERATOR ALGEBRAS FRACTIONAL POSITIVITY AND THE QUANTUM MOMENT PROBLEM

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Dosi A.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.363, sa.2, ss.801-856, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 363 Sayı: 2
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1090/s0002-9947-2010-05145-1
  • Dergi Adı: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.801-856
  • Anahtar Kelimeler: Local operator algebra, quantum system, quantum moment problem, fractional space, fractional positivity, SPACES
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

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.