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- W4313348352 abstract "Motivated by the results involving Drazin inverses of Patrício and Puystjens, we investigate the relevant results for pseudo Drazin invertibility and generalized Drazin invertibility in two semigroups of Banach algebras. Given a Banach algebra $mathcal{A}$ and $e^2=ein mathcal{A}$, we firstly establish the relation between pseudo Drazin invertibility (resp., generalized Drazin invertibility) of elements in $emathcal{A}e$ and $emathcal{A}e+1-e$. Then this result leads to a remarkable behavior of pseudo Drazin invertibility (resp., generalized Drazin invertibility) between the operators in the semigroup $AA^{-}mathscr{B}(Y)AA^{-}+I_Y-AA^{-}$ and the semigroup $A^{=}Amathscr{B}(X)A^{=}A+I_X-A^{=}A$, where $A^{-}, A^{=}in mathscr{B}(Y,X)$ are inner inverses of $Ain mathscr{B}(X,Y)$." @default.
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- W4313348352 date "2023-08-15" @default.
- W4313348352 modified "2023-09-26" @default.
- W4313348352 title "Generalized invertibility in two semigroups of Banach algebras" @default.
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- W4313348352 doi "https://doi.org/10.15672/hujms.1099257" @default.
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