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arXiv 2212.020122022-12math.FA

闭值域正正规算子及其乘积

Closed-range posinormal operators and their products

Paul Bourdon, Carlos Kubrusly, Trieu Le, Derek Thompson

发表信息：: Linear Algebra and its Applications, 671 (2023), 38-58

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AI总结：

本文研究正正规算子乘积保持正正规性的条件，给出闭值域的必要充分条件及可交换闭值域情形下的充分条件，并讨论其与 EP 算子的关系，给出 Hartwig-Katz 定理的新证明。

摘要：

我们聚焦于两个与“两个正正规算子的乘积何时为正正规算子”这一问题相关的问题，给出（1）正正规算子具有闭值域的必要条件和充分条件，以及（2）可交换的闭值域正正规算子的乘积为正正规且具有闭值域的充分条件。我们还讨论了正正规算子与 EP 算子（以及 hypo-EP 算子）之间的关系，最后给出 Hartwig-Katz 定理的一个新证明，该定理刻画了 $\CC^n$ 上正正规算子的乘积何时为正正规算子。

英文摘要：

We focus on two problems relating to the question of when the product of two posinormal operators is posinormal, giving (1) necessary conditions and sufficient conditions for posinormal operators to have closed range, and (2) sufficient conditions for the product of commuting closed-range posinormal operators to be posinormal with closed range. We also discuss the relationship between posinormal operators and EP operators (as well as hypo-EP operators), concluding with a new proof of the Hartwig-Katz Theorem, which characterizes when the product of posinormal operators on $\CC^n$ is posinormal.

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