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<p>We present a new version of an invertibility result for operators satisfying a lower bound condition. The result states that any bounded operator on a reflexive Banach space, which satisfies the lower bound condition, can be extended to a larger reflexive Banach space where it becomes invertible. Furthermore, we provide applications to <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(C_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-semigroups.</p>

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On the invertibility of bounded operators with a lower bound on reflexive Banach spaces, and applications to \(C_{0}\)-semigroups

  • 期刊论文

  • 发表日期：

    2026年1月4日

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  • Belabbas Madani

摘要

We present a new version of an invertibility result for operators satisfying a lower bound condition. The result states that any bounded operator on a reflexive Banach space, which satisfies the lower bound condition, can be extended to a larger reflexive Banach space where it becomes invertible. Furthermore, we provide applications to \(C_{0}\) C 0 -semigroups.