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<p>We reconsider studies of Toeplitz operators on function spaces (the weighted Bergman space, the generalized derivative Hardy space) and the H-Toeplitz operators on the Bergman space. Past studies have considered the presence or absence of hyponormality or questions of contractivity or expansivity; we provide structure theorems for these operators that allow us to recapture, and often considerably improve, these results. In some cases these operators or their adjoints are actually in more restrictive classes, such as subnormal or moment infinitely divisible (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_422_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {MID}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">MID</mi> </math></EquationSource> </InlineEquation>).</p>

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Toeplitz operators on several function spaces: decompositions yielding subnormality

  • 期刊论文

  • 发表日期：

    2025年4月17日

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  • Chafiq Benhida,
  • George R. Exner,
  • Ji Eun Lee,
  • Jongrak Lee

摘要

We reconsider studies of Toeplitz operators on function spaces (the weighted Bergman space, the generalized derivative Hardy space) and the H-Toeplitz operators on the Bergman space. Past studies have considered the presence or absence of hyponormality or questions of contractivity or expansivity; we provide structure theorems for these operators that allow us to recapture, and often considerably improve, these results. In some cases these operators or their adjoints are actually in more restrictive classes, such as subnormal or moment infinitely divisible ( \(\mathcal {MID}\) MID ).