Hankel矩阵与复多项式的算子系统
The Operator Systems of Hankel Matrices and Complex Polynomials
- Purdue University（普渡大学）
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AI总结：
本文研究有限Hankel矩阵与复多项式的算子系统结构，建立两者对偶间的单位完全序同构，并证明多项式系统极小、Hankel系统极大，进而用完全正映射刻画分块Hankel矩阵的正性。
AI中文摘要：
我们研究了有限Hankel矩阵的算子系统结构及其与实数轴上复多项式的联系。利用多项式矩阵谱分解，我们建立了(n+1)×(n+1)Hankel矩阵的算子系统与次数至多为2n的多项式算子系统的对偶之间的单位完全序同构。我们还证明了复多项式的算子系统是极小的，而Hankel算子系统是极大的。作为应用，我们刻画了以C*-代数中元素为系数的分块Hankel矩阵的正性，其条件由多项式算子系统上的完全正映射给出。
英文摘要：
We investigate the operator system structure of finite Hankel matrices and its connection with complex polynomials on the real line. Using polynomial matrix spectral factorization, we establish a unital complete order isomorphism between the operator system of (n + 1) x (n + 1) Hankel matrices and the dual of the operator system of polynomials of degree at most 2n. We also show that the operator system of complex polynomials is minimal, while the Hankel operator system is maximal. As an application, we characterize positivity of block Hankel matrices with entries in a C*-algebra in terms of completely positive maps on the polynomial operator system.
