Completely bounded kernels

Abstract

We introduce completely bounded kernels taking values in L(A,B) where A and B are C*-algebras. We show that if 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.Comment: 22 pages. Fixed oversight in previous version. To appear in Acta Scientiarum Mathematicarum (Szeged) for the 100th anniversary of the birth of Bela Sz.-Nag