Scholarlink

<p>We establish in this paper several descriptions of Kato type semi-B-Fredholm(<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\hbox{B}_{+}\)</EquationSource> </InlineEquation>-Fredholm or <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\hbox{B}_{-}\)</EquationSource> </InlineEquation>-Fredholm) and semi-B-Browder(<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\hbox{B}_{+}\)</EquationSource> </InlineEquation>-Browder or <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\hbox{B}_{-}\)</EquationSource> </InlineEquation>-Browder) linear relations in Banach spaces. These generalize the corresponding results of Cvetkovic and Zivkovic-Zlatanovic (Complex Anal Oper Theory 11:1425–1449, 2017) for bounded operators. We also study the interrelations between semi-B-Fredholm linear relations and semi-B-Browder linear relations. Among other things, we show that a linear relation <i>T</i> is <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\hbox{B}_{+}\)</EquationSource> </InlineEquation>-Browder (resp. <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\hbox{B}_{-}\)</EquationSource> </InlineEquation>-Browder) if and only if <i>T</i> is <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\hbox{B}_{+}\)</EquationSource> </InlineEquation>-Fredholm (resp. <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\hbox{B}_{-}\)</EquationSource> </InlineEquation>-Fredholm) and <i>T</i> (resp. the adjoint of <i>T</i>) has the SVEP at 0. We also consider as an application, the study of B-Fredholm <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(2\times 2\)</EquationSource> </InlineEquation> upper-triangular linear relation matrices.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Characterization of semi-B-Browder linear relations via SVEP

  • 期刊论文

  • 发表日期：

    2026年1月27日

查看全文
  • Teresa Álvarez,
  • Sonia Keskes

摘要

We establish in this paper several descriptions of Kato type semi-B-Fredholm( \(\hbox{B}_{+}\) -Fredholm or \(\hbox{B}_{-}\) -Fredholm) and semi-B-Browder( \(\hbox{B}_{+}\) -Browder or \(\hbox{B}_{-}\) -Browder) linear relations in Banach spaces. These generalize the corresponding results of Cvetkovic and Zivkovic-Zlatanovic (Complex Anal Oper Theory 11:1425–1449, 2017) for bounded operators. We also study the interrelations between semi-B-Fredholm linear relations and semi-B-Browder linear relations. Among other things, we show that a linear relation T is \(\hbox{B}_{+}\) -Browder (resp. \(\hbox{B}_{-}\) -Browder) if and only if T is \(\hbox{B}_{+}\) -Fredholm (resp. \(\hbox{B}_{-}\) -Fredholm) and T (resp. the adjoint of T) has the SVEP at 0. We also consider as an application, the study of B-Fredholm \(2\times 2\) upper-triangular linear relation matrices.