ArticleOriginal scientific text
Title
Dilation theorems for completely positive maps and map-valued measures
Authors 1, 1, 1
Affiliations
- Faculty of Mathematics, Łódź University, ul. Banacha 22, 90-238 Łódź, Poland
Abstract
The Stinespring theorem is reformulated in terms of conditional expectations in a von Neumann algebra. A generalisation for map-valued measures is obtained.
Keywords
completely positive map, von Neumann algebra, dilation, map-valued measure
Bibliography
- L. Accardi and M. Ohya, Compound channels, transition expectations and liftings, preprint.
- O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics, I, II New York-Heidelberg-Berlin, Springer, (1979).
- D. E. Evans and J. T. Lewis, Dilation of irreversible evolutions in algebraic quantum theory, Communications of the Dublin Institute for Advanced Studies, Series A (Theoretical Physics) 24 (1977).
- E. Hensz-Chądzyńska, R. Jajte and A. Paszkiewicz, Dilation theorems for positive operator-valued measures, Probab. Math. Statist. 17 (1997), 365-375.
- K. R. Parthasarathy, A continuous time version of Stinespring's theorem on completely positive maps, Quantum probability and Applications V, Proceedings, Heidelberg 1988, L. Accardi, W. von Waldenfels (eds.), Lecture Notes Math., Springer-Verlag (1988).
- W. F. Stinespring, Positive functions on C*-algebras, Proc. Amer. Math. Soc. 6 (1965), 211-216.
- S. Strătilă, Modular theory in operator algebras, Editura Academiei, Bucuresti, Abacus Press (1981).
- S. Strătilă and L. Zsidó, Lectures on von Neumann algebras, Editura Academiei, Bucuresti, (1979).
- B. Sz.-Nagy, Extensions of linear transformations in Hilbert space which extend beyond this space, Appendix to: F. Riesz and B. Sz.-Nagy, Functional Analysis, Frederick Ungar Publishing Co.
- M. Takesaki, Theory of operator algebras, I, Springer, Berlin-Heidelberg-New York (1979).
Pages:
231-239
Main language of publication
English
Published
1998
Exact and natural sciences