Abstract. We introduce completely bounded kernels taking values in ${\cal L}({\cal A}, {\cal B})$ where ${\cal A}$ and ${\cal B}$ are $C^*$-algebras. We show that if ${\cal B}$ is injective such kernels have a Kolmogorov decomposition precisely when they can be scaled to be completely contractive, and that this is automatic when the index set is countable.
AMS Subject Classification
(1991): 46L07; 46L08, 46E22, 46B20
Keyword(s):
completely bounded kernels,
hermitian kernels,
Kolmogorov decomposition
Received November 29, 2012, and in revised form December 14, 2012. (Registered under 103/2012.)
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