# Dilation theorems for completely positive maps and map-valued measures

Ewa Hensz-Chądzyńska; Ryszard Jajte; Adam Paszkiewicz

Banach Center Publications (1998)

- Volume: 43, Issue: 1, page 231-239
- ISSN: 0137-6934

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topHensz-Chądzyńska, Ewa, Jajte, Ryszard, and Paszkiewicz, Adam. "Dilation theorems for completely positive maps and map-valued measures." Banach Center Publications 43.1 (1998): 231-239. <http://eudml.org/doc/208843>.

@article{Hensz1998,

abstract = {The Stinespring theorem is reformulated in terms of conditional expectations in a von Neumann algebra. A generalisation for map-valued measures is obtained.},

author = {Hensz-Chądzyńska, Ewa, Jajte, Ryszard, Paszkiewicz, Adam},

journal = {Banach Center Publications},

keywords = {completely positive map; von Neumann algebra; dilation; map-valued measure; map-valued measures; spectral measure; Stinespring theorem; conditional expectations in a von Neumann algebra; operator-valued measure; ultra weak topology},

language = {eng},

number = {1},

pages = {231-239},

title = {Dilation theorems for completely positive maps and map-valued measures},

url = {http://eudml.org/doc/208843},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Hensz-Chądzyńska, Ewa

AU - Jajte, Ryszard

AU - Paszkiewicz, Adam

TI - Dilation theorems for completely positive maps and map-valued measures

JO - Banach Center Publications

PY - 1998

VL - 43

IS - 1

SP - 231

EP - 239

AB - The Stinespring theorem is reformulated in terms of conditional expectations in a von Neumann algebra. A generalisation for map-valued measures is obtained.

LA - eng

KW - completely positive map; von Neumann algebra; dilation; map-valued measure; map-valued measures; spectral measure; Stinespring theorem; conditional expectations in a von Neumann algebra; operator-valued measure; ultra weak topology

UR - http://eudml.org/doc/208843

ER -

## References

top- [1] L. Accardi and M. Ohya, Compound channels, transition expectations and liftings, preprint.
- [2] O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics, I, II New York-Heidelberg-Berlin, Springer, (1979). Zbl0421.46048
- [3] 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).
- [4] E. Hensz-Chądzyńska, R. Jajte and A. Paszkiewicz, Dilation theorems for positive operator-valued measures, Probab. Math. Statist. 17 (1997), 365-375. Zbl0897.46030
- [5] 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).
- [6] W. F. Stinespring, Positive functions on C*-algebras, Proc. Amer. Math. Soc. 6 (1965), 211-216.
- [7] S. Strătilă, Modular theory in operator algebras, Editura Academiei, Bucuresti, Abacus Press (1981). Zbl0504.46043
- [8] S. Strătilă and L. Zsidó, Lectures on von Neumann algebras, Editura Academiei, Bucuresti, (1979). Zbl0391.46048
- [9] 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.
- [10] M. Takesaki, Theory of operator algebras, I, Springer, Berlin-Heidelberg-New York (1979). Zbl0436.46043

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