摘要
We prove that every homomorphism of the algebra P<sub><em>n</em></sub> 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 <span style="white-space:normal;">P</span><sub style="white-space:normal;"><em>n</em></sub> generate completely positive maps over the algebras <em>C</em>(T<sup><em>n</em></sup>)and <em>M</em><sub>2</sub>(<em>C</em>(T<sup><em>n</em></sup>)).
We prove that every homomorphism of the algebra P<sub><em>n</em></sub> 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 <span style="white-space:normal;">P</span><sub style="white-space:normal;"><em>n</em></sub> generate completely positive maps over the algebras <em>C</em>(T<sup><em>n</em></sup>)and <em>M</em><sub>2</sub>(<em>C</em>(T<sup><em>n</em></sup>)).
