Journal article
Positive elements in the algebra of the quantum moment problem
Probability theory and related fields, Vol.89(2), pp.131-139
06/1991
DOI: 10.1007/BF01366901
Abstract
LetA denote the extended Weyl algebra,A0⊂A, the Weyl algebra. It is well known that every element ofA of the formA=ΣB *k B k is positive. We prove that the converse implication also holds: Every positive elementA inA has a quadratic sum factorization for some finite set of elements (B k ) inA. The corresponding result is not true for the subalgebraA0. We identify states onA0 which do not extend to states onA. It follows from a result of Powers (and Arveson) that such states onA0 cannot be completely positive. Our theorem is based on a certain regularity property for the representations which are generated by states onA, and this property is not in general shared by representations generated by states defined only on the subalgebraA0.
Details
- Title: Subtitle
- Positive elements in the algebra of the quantum moment problem
- Creators
- Palle E. T JorgensenRobert T Powers
- Resource Type
- Journal article
- Publication Details
- Probability theory and related fields, Vol.89(2), pp.131-139
- DOI
- 10.1007/BF01366901
- ISSN
- 0178-8051
- eISSN
- 1432-2064
- Language
- English
- Date published
- 06/1991
- Academic Unit
- Mathematics
- Record Identifier
- 9983985925002771
Metrics
27 Record Views