论文标题
操作者理论中有条件积极的确定性
Conditionally positive definiteness in operator theory
论文作者
论文摘要
在本文中，我们广泛研究了有条件的正定运算符的类别，即产生有条件的正定序列。该课程本身包含亚正常运营商，$ 2 $ - 和$ 3 $ - iSomerties，还有更多。本文的很大一部分致力于研究有条件的积极确定的指数增长序列，重点是为其积极的确定性找到标准，在这些标准中，这两个概念在半群中都可以理解。结果，我们为有条件的确定运算符获得了半光谱和扩张类型表示。我们还表明，有条件积极的确定运算符类别在夺取权力的运作下关闭。在Agler的遗传功能演算的基础上，我们为此类的运算符构建了一个$ l^{\ infty}（m）$ - 功能分积分，其中$ m $是相关的半光谱度量。我们为涉及多项式和分析功能的不平等现象提供了多种应用。此外，我们为有条件的积极算子提供了新的必要条件，使其成为良好的收缩（包括伸缩性算法）。
In this paper we extensively investigate the class of conditionally positive definite operators, namely operators generating conditionally positive definite sequences. This class itself contains subnormal operators, $2$- and $3$-isometries and much more beyond them. Quite a large part of the paper is devoted to the study of conditionally positive definite sequences of exponential growth with emphasis put on finding criteria for their positive definiteness, where both notions are understood in the semigroup sense. As a consequence, we obtain semispectral and dilation type representations for conditionally positive definite operators. We also show that the class of conditionally positive definite operators is closed under the operation of taking powers. On the basis of Agler's hereditary functional calculus, we build an $L^{\infty}(M)$-functional calculus for operators of this class, where $M$ is an associated semispectral measure. We provide a variety of applications of this calculus to inequalities involving polynomials and analytic functions. In addition, we derive new necessary and sufficient conditions for a conditionally positive definite operator to be a subnormal contraction (including a telescopic one).
