ON BOUNDEDNESS AND COMPLETE POSITIVITY OF MAPS ON BANACH ALGEBRAS

N. B. Okelo

Abstract


Let and  be algebras, and   be by  matrices with entries from and  respectively and  be a linear map, then we define maps    by  for all natural numbers . We determine conditions under which   is positive for all                                                                                                                                

Keywords: Hermitian maps, unital -homomorphism and completely positive maps.


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References


Arveson W.B., An Invitation to C^*-Algebras, Springer-Verlag, Berlin 1998 (reprinted).

Blecher D.P. and Paulsen V.I., Tensor Products of Operator Spaces, Journal of Functional Analysis. 99(1991), 262-292.

Choi M.D., Completely positive linear maps on complex matrices, Linear Algebra and Appl., 10 (1975), 285-290.

Choi M.D. , Positive Linear Maps on C^*-algebras, Canad. J. Math., 24(1972), 520-529.

Conway J.B., A Course in Functional Analysis, Second Edition, Springer-Verlag, Berlin 1990.

Gheondea A. and Kavruk A.S., Absolute Continuity of Operator Valued Completely Positive Maps on C^*algebras, J. Math. Phys., 50 (2008), 022-102.

Murphy J. G., C^*-algebras and Operator Theory, Academic Press Inc., Oval Road, London, 1990.

Naimark M.A., Positive Definite Operator Functions on a Commutative Group [Russian], Izv. Akad. Nauk SSSR, 7(1943), 237-244.

Paulsen V.I., Completely Bounded Maps and Operator Algebras, Cambridge studies in advance Mathematics 78, Cambridge University Press, Cambridge, 2003.

Rajendra B., Positive Definite Matrices. Princeton Series in Applied Mathematics. Princeton University Press, Princeton and Oxford, 2007.

Stinespring W.F., Positive functions on C^*-algebras, Proc. Amer. Math. Soc., 6(1955), 211-216.


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