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 introduc...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>)).展开更多
In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presen...In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.展开更多
文摘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>)).
基金supported partially by the China Scholarship Council and the Science Foundation of Tianjin Polytechnic Universitysupported in part by the Natural Science Foundation Project of Chongqing,China(Grant No.CSTC2011JJA00024)+1 种基金the Research Project of Science and Technology of Chongqing Education Commission,China(Grant No.KJ120625)the Fund of Chongqing Normal University,China(Grant Nos.10XLR017 and 2011XLZ07)
文摘In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.
