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

Abstract

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

How to cite

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Hensz-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

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  1. [1] L. Accardi and M. Ohya, Compound channels, transition expectations and liftings, preprint. 
  2. [2] O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics, I, II New York-Heidelberg-Berlin, Springer, (1979). Zbl0421.46048
  3. [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. [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. [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. [6] W. F. Stinespring, Positive functions on C*-algebras, Proc. Amer. Math. Soc. 6 (1965), 211-216. 
  7. [7] S. Strătilă, Modular theory in operator algebras, Editura Academiei, Bucuresti, Abacus Press (1981). Zbl0504.46043
  8. [8] S. Strătilă and L. Zsidó, Lectures on von Neumann algebras, Editura Academiei, Bucuresti, (1979). Zbl0391.46048
  9. [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. [10] M. Takesaki, Theory of operator algebras, I, Springer, Berlin-Heidelberg-New York (1979). Zbl0436.46043

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