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<p>This paper explores the properties of two novel operators, the 2-Laurent operator and the 2-Toeplitz operator, acting on the Lebesgue space and the Hardy space, respectively. These operators are characterized by matrices with alternating constant entries along each diagonal parallel to the main diagonal. They are significant because they reduce to the classical Laurent and Toeplitz operators as special cases. The paper provides several important results, including characterizations of these operators, and also introduces generalizations for any natural number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_464_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(k \ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. These generalizations, termed the <i>k</i>-Laurent and <i>k</i>-Toeplitz operators, encompass the 2-Laurent and 2-Toeplitz operators as particular instances when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_464_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(k=2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Properties of 2-Toeplitz operator and its generalization

  • 期刊论文

  • 发表日期：

    2025年7月21日

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  • Bhawna Gupta,
  • Jyoti Bhola

摘要

This paper explores the properties of two novel operators, the 2-Laurent operator and the 2-Toeplitz operator, acting on the Lebesgue space and the Hardy space, respectively. These operators are characterized by matrices with alternating constant entries along each diagonal parallel to the main diagonal. They are significant because they reduce to the classical Laurent and Toeplitz operators as special cases. The paper provides several important results, including characterizations of these operators, and also introduces generalizations for any natural number \(k \ge 2\) k ≥ 2 . These generalizations, termed the k-Laurent and k-Toeplitz operators, encompass the 2-Laurent and 2-Toeplitz operators as particular instances when \(k=2\) k = 2 .