Normal forms on partial *-algebras
(1991) Journal of Mathematical Physics — Vol. 32, n° 8, p. 2074-2081 (1991)
Files
No attached file found for this publication.
Details
- Authors
Antoine, Jean-Pierre 
- Abstract
- (en) In the algebraic formulation of quantum theories, a state is often represented by a normal linear functional on some *‐algebra A of operators on a Hilbert space, i.e., a functional of the form f(X)=Tr T X for some trace class operator X. The question is whether every strongly positive (i.e., positive on positive elements) linear functional is normal. Criteria for this statement to be true are well known in the case where A is a *‐algebra of bounded operators (C*‐ or W*‐algebra) or a *‐algebra of unbounded operators (O*‐algebra). Those results are extended to the case where A is a (weak) partial *‐algebra of closable operators, both for linear functionals and for sesquilinear forms.
- Affiliations
Fukuoka University Department of Applied Mathematics
Citations
Antoine, J.-P., & Inoue, A. (1991). Normal forms on partial *-algebras. Journal of Mathematical Physics, 32(8), 2074-2081. https://doi.org/10.1063/1.529508 (Original work published 1991)