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<p>In this paper, we introduce the notion of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-left invertibility (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-right invertibility) which is a generalization of <i>m</i>-left invertibility (<i>m</i>-right invertibility) on a Hilbert space, we study basic properties of this notion. Furthermore, we show that the power of any <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-isometric operator is <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-isometric. We investigate the local spectrum of the class of <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-isometric operators, and we prove that every <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-isometric operator has the property <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\((\beta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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The notion of \(\infty \)-invertibility and \(\infty \)-isometric operators

  • 期刊论文

  • 发表日期：

    2025年8月6日

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  • Souhaib Djaballah,
  • Messaoud Guesba

摘要

In this paper, we introduce the notion of \(\infty \) ∞ -left invertibility ( \(\infty \) ∞ -right invertibility) which is a generalization of m-left invertibility (m-right invertibility) on a Hilbert space, we study basic properties of this notion. Furthermore, we show that the power of any \(\infty \) ∞ -isometric operator is \(\infty \) ∞ -isometric. We investigate the local spectrum of the class of \(\infty \) ∞ -isometric operators, and we prove that every \(\infty \) ∞ -isometric operator has the property \((\beta )\) ( β ) .