TITLE:
On Kadison’s Similarity Problem for Homomorphisms of the Algebra of Complex Polynomials
AUTHORS:
Joachim Moussounda Mouanda
KEYWORDS:
Inequalities for Sums, Fourier Coefficients, Operator Theory, Polynomials
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.11 No.9,
September
22,
2021
ABSTRACT: We prove that every homomorphism of the algebra Pn 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 Pn generate completely positive maps over the algebras C(Tn)and M2(C(Tn)).