Partially Commutative Moment Problems | Zendy

Borchers H. J. | Zendy; Yngvason Jakob | Zendy

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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.

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