重数2的加权移位的平方根

Pub Date : 2022-12-23 DOI:10.4153/S000843952200073X

Chanaka Kottegoda, Trieu Le, Tomas Miguel Rodriguez

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引用次数: 0

摘要

摘要给定重数为2的加权移位T，我们研究了T的所有平方根的集合$\sqrt｛T｝$。我们确定了权重序列上的充要条件，使该集合是非空的。我们证明了当满足这样的条件时，$\sqrt｛T｝$包含一类特殊的算子。我们还获得了$\sqrt｛T｝$中所有运算符的完整描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Square roots of weighted shifts of multiplicity two

Abstract Given a weighted shift T of multiplicity two, we study the set $\sqrt {T}$ of all square roots of T. We determine necessary and sufficient conditions on the weight sequence so that this set is non-empty. We show that when such conditions are satisfied, $\sqrt {T}$ contains a certain special class of operators. We also obtain a complete description of all operators in $\sqrt {T}$ .

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