Weighted shifts relevant to CPD matrices and their examples

초록

In 1990 R. Curto introduced the notion of n-hyponormality which provides a bridge between subnormal and hyponormal operators. The study of n-hyponormal weighted shifts has been well developed by several mathematicians. In this paper we introduce a property CP(n) for weighted shifts related to (n + 1) x (n + 1) conditionally positive definite matrices, which generalizes n-hyponormality for weighted shifts. First the flatness of a weighted shift with properties CP (2) and CP (3) is considered, yielding a result which generalizes previous work. A formula for property CP(n) is constructed, which distinguishes the classes of weighted shifts with property CP(n). We introduce an algorithm to construct weighted shifts with property CP(n) and detect the structure related to property CP(n). Finally, we discuss property CP(n) of a homographic-type weighted shift with a constraint condition. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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