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<p>In this paper, the essential criteria for the hyponormality and quasinormality of the unbounded Toeplitz operator <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1703_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_{\varphi }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>φ</mi> </msub> </math></EquationSource> </InlineEquation> where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1703_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation> represents a harmonic polynomial in the Fock-Sobolev space <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1703_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">\(F^{2, m}(\mathbb {C})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>F</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>m</mi> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> has been established. The study shows that quasinormality does not inherently imply hyponormality for harmonic polynomials. Moreover, the paper identifies an additional necessary condition under which quasinormality does lead to the hyponormality.</p>

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Hyponormality and Quasinormality of Unbounded Toeplitz operators on the Fock-Sobolev Space

  • 期刊论文

  • 发表日期：

    2025年5月19日

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  • Anuradha Gupta,
  • Kajal Negi

摘要

In this paper, the essential criteria for the hyponormality and quasinormality of the unbounded Toeplitz operator \(T_{\varphi }\) T φ where \(\varphi \) φ represents a harmonic polynomial in the Fock-Sobolev space \(F^{2, m}(\mathbb {C})\) F 2 , m ( C ) has been established. The study shows that quasinormality does not inherently imply hyponormality for harmonic polynomials. Moreover, the paper identifies an additional necessary condition under which quasinormality does lead to the hyponormality.