Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The G-Drazin Inverse of an Operator Matrix over Banach Spaces

  • Farzaneh Tayebi (Department of Mathematics, Statistics and Computer Science, Semnan University) ;
  • Nahid Ashrafi (Department of Mathematics, Statistics and Computer Science, Semnan University) ;
  • Rahman Bahmani (Department of Mathematics, Statistics and Computer Science, Semnan University) ;
  • Marjan Sheibani Abdolyousefi (Farzanegan Campmus, Semnan University)
  • Received : 2023.06.29
  • Accepted : 2024.01.22
  • Published : 2024.06.30
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Abstract

Let 𝒜 be a Banach algebra. An element a ∈ 𝒜 has generalized Drazin inverse if there exists b ∈ 𝒜 such that b = bab, ab = ba, a - a2b ∈ 𝒜qnil. New additive results for the generalized Drazin inverse of an operator over a Banach space are presented. we extend the main results of a paper of Shakoor, Yang and Ali from 2013 and of Wang, Huang and Chen from 2017. Appling these results to 2×2 operator matrices we also generalize results of a paper of Deng, Cvetković-Ilić and Wei from 2010.

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References

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