In the current research paper, we introduce the concept of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-pseudo quasi-Fredholm and explore its relationship with the decomposition akin to the Kato type operators. This decomposition yields a result regarding the stability of this class of operators under perturbations by nilpotent operators. Additionally, we present a new decomposition for the new class of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-pseudo semi B-Weyl operators. Through this property, we demonstrate that A is a <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-pseudo lower semi B-Weyl operator if, and only if, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$A = D + K-H$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <mo>=</mo> <mi>D</mi> <mo>+</mo> <mi>K</mi> <mo>-</mo> <mi>H</mi> </mrow> </math></EquationSource> </InlineEquation> where K is finite-dimensional and D is a <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-pseudo lower semi B-Browder operator for all <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$H \in \mathcal {B(X)}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo>∈</mo> <mrow> <mi mathvariant="script">B</mi> <mo stretchy="false">(</mo> <mi mathvariant="script">X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> such that <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$\Vert H\Vert <\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">‖</mo> <mi>H</mi> <mo stretchy="false">‖</mo> <mo><</mo> <mi>δ</mi> </mrow> </math></EquationSource> </InlineEquation>.

Characterization of B-Browder and $\delta $-pseudo quasi-Fredholm operators in Banach spaces

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发表日期：

2026年2月23日

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Bilel Trabelsi

摘要

In the current research paper, we introduce the concept of $\delta $ $δ$ -pseudo quasi-Fredholm and explore its relationship with the decomposition akin to the Kato type operators. This decomposition yields a result regarding the stability of this class of operators under perturbations by nilpotent operators. Additionally, we present a new decomposition for the new class of $\delta $ $δ$ -pseudo semi B-Weyl operators. Through this property, we demonstrate that A is a $\delta $ $δ$ -pseudo lower semi B-Weyl operator if, and only if, $A = D + K-H$ $A = D + K - H$ where K is finite-dimensional and D is a $\delta $ $δ$ -pseudo lower semi B-Browder operator for all $H \in \mathcal {B(X)}$ $H \in B (X)$ such that $\Vert H\Vert <\delta $ $‖ H ‖ < δ$ .

Characterization of B-Browder and \(\delta \)-pseudo quasi-Fredholm operators in Banach spaces

摘要