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<p>The purpose of this paper is to provide some perturbation results of the single valued extension property at a point of the semi B-Fredholm resolvent set of closed operator, under a power finite-rank commuting operator which satisfies certain conditions. Additionally, we consider a closed densely-defined linear operator <i>T</i> represented as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\displaystyle T=\Gamma (K)=K(I-K^{*}K)^{-\frac{1}{2}},\)</EquationSource> <EquationSource Format="MATHML"><math> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mi>T</mi> <mo>=</mo> <mi mathvariant="normal">Γ</mi> <mrow> <mo stretchy="false">(</mo> <mi>K</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mi>K</mi> <msup> <mrow> <mo stretchy="false">(</mo> <mi>I</mi> <mo>-</mo> <msup> <mi>K</mi> <mrow> <mrow /> <mo>∗</mo> </mrow> </msup> <mi>K</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>,</mo> </mrow> </mstyle> </math></EquationSource> </InlineEquation> where <i>K</i> is a pure quasi-normal contraction defined on a Hilbert space and we prove, in this stage, that the map <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation> preserves this property at the point 0 for some classes of operators.</p>

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Some stability results of the single valued extension property for a closed operator in Hilbert space

  • 期刊论文

  • 发表日期：

    2026年4月22日

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  • Monia Boudhief

摘要

The purpose of this paper is to provide some perturbation results of the single valued extension property at a point of the semi B-Fredholm resolvent set of closed operator, under a power finite-rank commuting operator which satisfies certain conditions. Additionally, we consider a closed densely-defined linear operator T represented as \(\displaystyle T=\Gamma (K)=K(I-K^{*}K)^{-\frac{1}{2}},\) T = Γ ( K ) = K ( I - K ∗ K ) - 1 2 , where K is a pure quasi-normal contraction defined on a Hilbert space and we prove, in this stage, that the map \(\Gamma \) Γ preserves this property at the point 0 for some classes of operators.