Journal of Operator Theory

Volume 42, Issue 1, Summer 1999 pp. 83-102.

Strong Feller semigroups on

$C^*$ -algebras

Authors: Jean-Luc Sauvageot
Author institution: Institut de Mathematiques, Algebres d'operateurs et representations, Universite Pierre et Marie Curie, Boite 191, 4 place Jussieu, F--75252 Paris Cedex 05, France

Summary: On a given

$C^*$ -algebra, the existence of a strong Feller semigroup is equivalent to the existence of an approximation of the identity by weakly compact completely positive endomorphisms. As a corollary, there are strong Feller semigroups on any nuclear

$C^*$ -algebra, but one can find also strong Feller semigroups on non nuclear

$C^*$ -algebras.

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