论文标题
有条件的积极确定性，作为K- - 基本规范与N缩的桥梁
Conditional positive definiteness as a bridge between k-hyponormality and n-contractivity
论文作者
论文摘要
对于序列，$α\ equiv \ {α_n\} _ {n = 0}^{\ infty} $的正实数（称为权重），我们研究加权移动型$w_α$具有力矩无限划分的属性（$ \ mathcal {midcal {mid} $）;也就是说，对于任何$ p> 0 $，schur power $w_α^p $都是次级正常。我们首先证明$w_α$是$ \ MATHCAL {MID} $，并且仅当某些无限矩阵$ \ logm_γ（0）$和$ \ log logm_γ（1）$是有条件的正定义（CPD）。在这里，$γ$是与$α$，$m_γ（0），m_γ（1）$相关的一系列时刻，是典型的汉克尔矩阵，其正半确定性决定了$w_α$的亚正态性，而$ \ log $的亚正态性则是计算的入门（即Schur或schur或hataMard）。接下来，我们使用有条件的积极确定性来建立$ K $ - 不正常和$ n $ - 合同性之间的新桥梁，该桥梁对两个众所周知的楼梯如何从不良性到亚正态相互作用阐明了重大新的启示。结果，我们证明，当所有$ p> 0 $，$ p> 0 $，$m_γ^p（0）$和$m_γ^p（1）$是cpd的，当所有$ p> 0 $，$ p> 0 $，$ p> 0 $，$ p> 0 $，$w_α$时。
For sequences $α\equiv \{α_n\}_{n=0}^{\infty}$ of positive real numbers, called weights, we study the weighted shift operators $W_α$ having the property of moment infinite divisibility ($\mathcal{MID}$); that is, for any $p > 0$, the Schur power $W_α^p$ is subnormal. We first prove that $W_α$ is $\mathcal{MID}$ if and only if certain infinite matrices $\log M_γ(0)$ and $\log M_γ(1)$ are conditionally positive definite (CPD). Here $γ$ is the sequence of moments associated with $α$, $M_γ(0),M_γ(1)$ are the canonical Hankel matrices whose positive semi-definiteness determines the subnormality of $W_α$, and $\log$ is calculated entry-wise (i.e., in the sense of Schur or Hadamard). Next, we use conditional positive definiteness to establish a new bridge between $k$--hyponormality and $n$--contractivity, which sheds significant new light on how the two well known staircases from hyponormality to subnormality interact. As a consequence, we prove that a contractive weighted shift $W_α$ is $\mathcal{MID}$ if and only if for all $p>0$, $M_γ^p(0)$ and $M_γ^p(1)$ are CPD.
