Journal of Jilin University Science Edition ›› 2020, Vol. 58 ›› Issue (3): 595-598.
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GUO Li, XU Xiaojie, GU Tianyu, YU Deyue, LEI Ming
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Abstract: Let a,b be two generalized Drazin invertible elements in a Banach algebra, ad be the generalized Drazin inverse of aand aπ=1-aad. We gave the expressions for the generalized Drazin [JP2]inverse of the sum a+b under some conditions such as abπ=a, bπbaπ=bπb, bπaπa2b=bπaπaba, bπaπb2a=bπaπbab etc by using the idempotent element in a Banach algebra.
Key words: generalized Drazin inverse, Banach algebra, quasinilpotent element
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GUO Li, XU Xiaojie, GU Tianyu, YU Deyue, LEI Ming. Relevant Results on Generalized DrazinInverses in a Banach Algebra[J].Journal of Jilin University Science Edition, 2020, 58(3): 595-598.
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http://xuebao.jlu.edu.cn/lxb/EN/Y2020/V58/I3/595
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