English

Completely bounded kernels

Operator Algebras 2012-12-17 v3 Functional Analysis

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.

Keywords

Cite

@article{arxiv.1001.3590,
  title  = {Completely bounded kernels},
  author = {Tirthankar Bhattacharyya and Michael A. Dritschel and Christopher S. Todd},
  journal= {arXiv preprint arXiv:1001.3590},
  year   = {2012}
}

Comments

22 pages. Fixed oversight in previous version. To appear in Acta Scientiarum Mathematicarum (Szeged) for the 100th anniversary of the birth of Bela Sz.-Nagy

R2 v1 2026-06-21T14:37:11.515Z