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<p>The defect operators carry the key information of the commuting isometric tuples. In many cases, the compactness of the defect operators implies the Fredholmness of the isometric tuples. In this paper, we characterize the compactness of the defect operators associated with Toeplitz tuples on the Hardy space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44146_2025_201_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^2(\mathbb {D}^n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">D</mi> </mrow> <mi>n</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> with inner symbols.</p>

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The compactness of defect operators for the commuting isometric tuples

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Miao He,
  • Zeyou Zhu

摘要

The defect operators carry the key information of the commuting isometric tuples. In many cases, the compactness of the defect operators implies the Fredholmness of the isometric tuples. In this paper, we characterize the compactness of the defect operators associated with Toeplitz tuples on the Hardy space \(H^2(\mathbb {D}^n)\) H 2 ( D n ) with inner symbols.