Scholarlink

<p>The Cauchy dual subnormality problem for 2-isometries has attracted the attention of researchers in recent years. In this article, we describe the problem and present a new counter-example to the problem by constructing a family of analytic, cyclic 2-isometric operators whose Cauchy dual is not subnormal. The said example is in contrast with the class of operators, recently found, whose Cauchy dual is subnormal. In the process, we employ the technique of realizing a 2-isometry as a shift operator on a suitable de Branges–Rovnyak space. The construction of the counter example involves some unwieldy computations around the roots of a polynomial of degree four. We therefore use numerical techniques with the help of SageMath to facilitate the computational work.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An example of a cyclic analytic 2-isometry whose Cauchy dual is not subnormal

  • 期刊论文

  • 发表日期：

    2025年8月31日

查看全文
  • Mandar N Khasnis,
  • Vinayak M Sholapurkar

摘要

The Cauchy dual subnormality problem for 2-isometries has attracted the attention of researchers in recent years. In this article, we describe the problem and present a new counter-example to the problem by constructing a family of analytic, cyclic 2-isometric operators whose Cauchy dual is not subnormal. The said example is in contrast with the class of operators, recently found, whose Cauchy dual is subnormal. In the process, we employ the technique of realizing a 2-isometry as a shift operator on a suitable de Branges–Rovnyak space. The construction of the counter example involves some unwieldy computations around the roots of a polynomial of degree four. We therefore use numerical techniques with the help of SageMath to facilitate the computational work.