Opuscula Math. 29, no. 2 (2009), 139-145
http://dx.doi.org/10.7494/OpMath.2009.29.2.139

Opuscula Mathematica

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

Aurelian Gheondea
Ali Şamil Kavruk

Abstract. We point out a relation between the Arveson's Radon-Nikodým 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.

Keywords: Radon-Nikodým derivative, $$C^*$$-algebra, completely positive map, similarity.

Mathematics Subject Classification: 46L07.

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• Aurelian Gheondea
• Bilkent University, Department of Mathematics, 06800 Bilkent, Ankara, Turkey
• Institutul de Matematică al Academiei Române, C.P. 1-764, 014700 Bucureşti, România
• Ali Şamil Kavruk
• University of Houston, Department of Mathematics, Houston, TX 77204-3476, U.S.A.
• Received: 2008-12-12.
• Accepted: 2009-01-22.

Cite this article as:
Aurelian Gheondea, Ali Şamil Kavruk, A note on Radon-Nikodým derivatives and similarity for completely bounded maps, Opuscula Math. 29, no. 2 (2009), 139-145, http://dx.doi.org/10.7494/OpMath.2009.29.2.139

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