On Kadison’s Similarity Problem for Homomorphisms of the Algebra of Complex Polynomials

Abstract

We prove that every homomorphism of the algebra P n into the algebra of operators on a Hilbert space is completely bounded. We show that the contractive homomorphism introduced by Parrott, which is not completely contractive, is completely bounded (similar to a completely contractive homomorphism). We also show that homomorphisms of the algebra P n generate completely positive maps over the algebras C (T n )and M 2 ( C (T n )).