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The G-Drazin Inverse of an Operator Matrix over Banach Spaces

Nahid Ashrafi|Marjan Sheibani Abdolyousefi|Farzaneh Tayebi|Rahman Bahmani
경북대학교 자연과학대학 수학과|2024.06|Kyungpook Mathematical Journal|제64권 제2호|pp. 205-218|DOI 10.5666/KMJ.2024.64.2.205

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키워드

operator matrixadditive propertygeneralized Drazin inversespectral idempotent
주제분류수학

초록

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-a^2b ∈ A^(qnil). 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, Cvetkovic-Ilic and Wei from 2010.

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-a^2b ∈ A^(qnil). 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, Cvetkovic-Ilic and Wei from 2010.

참고문헌 (25)

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관련 논문AI추천

Group inverse and generalized Drazin inverse of block matrices in a Banach algebraDijana Mosic대한수학회 · 대한수학회보2014 · 제51권 제3호Weighted Moore-Penrose invertible and weighted EP Banach algebra elementsDijana Mosić, Dragan S. Djordjevic, Enrico Boasso대한수학회 · 대한수학회지2013 · 제50권 제6호The Drazin inverse of the sum of two productsAbdelaziz Tajmouati, Safae Alaoui Chrifi대한수학회 · 대한수학회논문집2022 · 제37권 제3호Weighted gDMP inverse of operators between Hilbert spacesDijana Mosic대한수학회 · 대한수학회보2018 · 제55권 제4호REPRESENTATION OF BOUNDED LINEAR OPERATORS WITH EQUAL SPECTRAL PROJECTIONS AT ZERODong-Jun Chen, Yun Zhang대한수학회 · 대한수학회논문집2010 · 제25권 제4호Note on the Generalized Invertibility of a-xyFapeng Du, Yifeng Xue경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제2호

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