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Partially Commutative Moment Problems
Author(s) -
Borchers H. J.,
Yngvason Jakob
Publication year - 1990
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19901450109
Subject(s) - mathematics , commutative property , hilbert space , pure mathematics , property (philosophy) , algebraic number , algebra over a field , algebraic structure , field (mathematics) , state (computer science) , ideal theory , commutative ring , mathematical analysis , philosophy , epistemology , algorithm
Partially commutative tensor algebras occur naturally in the algebraic formulation of Wightman field theory. A state on an algebra of this type leads via GNS‐construction to a partially commutative family of hermitean operators on Hilbert space. We discuss the question when these operators can be extended to self adjoint operators preserving the commutation properties and state a necessary and sufficient condition for the existence of such an extension in terms of a positivity property of the state.