Regular representations of completely bounded maps

B. V. Rajarama Bhat, Nirupama Mallick and K. Sumesh

Vol. 289 (2017), No. 2, 257–286

DOI: 10.2140/pjm.2017.289.257

Abstract

We study properties and the structure of some special classes of homomorphisms on $C^{\ast }$-algebras. These maps are $\ast$-preserving up to conjugation by a symmetry. Making use of these homomorphisms, we prove a new structure theorem for completely bounded maps from a unital $C^{\ast }$-algebra into the algebra of all bounded linear maps on a Hilbert space. Finally we provide alternative proofs for some of the known results about completely bounded maps and improve on them.

Keywords

$C^\ast$-algebra, completely bounded map, Hilbert $C^\ast$-module, Stinespring's theorem, $\ast$-homomorphism

Mathematical Subject Classification 2010

Primary: 46L07, 46L08

Secondary: 46L05

Milestones

Received: 6 October 2015

Accepted: 29 December 2016

Published: 19 June 2017