A note on Radon-Nikodym derivatives and similarity for completely bounded maps

• Autorzy: Gheondea A. , Kavruk A. S.
• Języki publikacji: EN

Abstrakty

EN

We point out a relation between the Arveson's Radon-Nikodym derivative and known similarity results for completely bounded maps. We also consider Jordan type decompositions coming out from Wittstock's Decomposition Theorem and illustrate, by an example, the nonuniqueness of these decompositions.

Słowa kluczowe

EN

Radon-Nikodym derivative; C*-algebra; completely positive map; similarity

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2009
• Tom: Vol. 29, no. 2
• Strony: 139--145
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Gheondea A.

autor

Kavruk A. S.

• Bilkent University Department of Mathematics 06800 Bilkent, Ankara, Turkey Institutul de Matematica al Academiei Romane C.P. 1-764, 014700 Bucuresti, Romania,

Bibliografia

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• [2] T. Constantinescu, A. Gheondea, Representations of Hermitian kernels by means of Krein spaces, Publ. RIMS Kyoto Univ. 33 (1997), 917–951.
• [3] E. Christensen, On non self adjoint representations of operator algebras, Amer. J. Math. 103 (1981), 817–834.
• [4] E.G. Effros, Z.-J. Ruan, Operator Spaces, The Clarendon Press, Oxford University Press, Oxford, 2000.
• [5] U. Haagerup, Solution of the similarity problem for cyclic representations of C*-algebras, Ann. Math. 18 (1983), 215–240.
• [6] D. Hadwin, Dilations and Hahn decompositions for linear maps, Canad. J. Math. 33 (1981), 826–839.
• [7] V. Paulsen, Completely Bounded Maps and Operator Algebras, Cambridge University Press, Cambridge, 2002.
• [8] W.F. Stinespring, Positive functions on C*-algebras, Proc. Amer. Math. Soc. 6 (1955), 211–216.
• [9] G. Wittstock, Ein operatorwertiger Hahn-Banach Satz, J. Funct. Anal. 40 (1981) 2, 127–150.