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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 3

The generalized Drazin inverse of operator matrices

Li Guo(Southeast University)0000-0003-3495-573X
Honglin Zou(Beihua University)0000-0002-0064-9729
Jianlong Chen(Hubei Normal University)
Sayfa
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Yayın Tarihi
2020-06-02
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As corollaries, several well-known results are generalized.

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Amaç & Hipotez:Representations for the generalized Drazin inverse of an operator matrix $\begin{pmatrix}A & B \\ C & D \end{pmatrix}$ are presented in terms of $A,B,C,D$ and the generalized Drazin inverses of $A,D$, under the condition that $BD^d=0,~\text{and}~BD^iC=0,~\text{for any nonnegative integer}~ i.$ Using the representation, we give a new additive result of the generalized Drazin inverse for two bounded linear operators $P,Q \in \mathbf{B}(X)$ with $PQ^{d}=0$ and $PQ^{i}P=0$, for any integer $i\geq 1$.
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Temel Bulgular & Veri:Representations for the generalized Drazin inverse of an operator matrix $\begin{pmatrix}A & B \\ C & D \end{pmatrix}$ are presented in terms of $A,B,C,D$ and the generalized Drazin inverses of $A,D$, under the condition that $BD^d=0,~\text{and}~BD^iC=0,~\text{for any nonnegative integer}~ i.$ Using the representation, we give a new additive result of the generalized Drazin inverse for two bounded linear operators $P,Q \in \mathbf{B}(X)$ with $PQ^{d}=0$ and $PQ^{i}P=0$, for any integer $i\geq 1$.
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Sonuç & Katkı:As corollaries, several well-known results are generalized.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Banach space · generalized Drazin inverse · operator matrix

Abstract

Representations for the generalized Drazin inverse of an operator matrix $\begin{pmatrix}A & B \\ C & D \end{pmatrix}$ are presented in terms of $A,B,C,D$ and the generalized Drazin inverses of $A,D$, under the condition that $BD^d=0,~\text{and}~BD^iC=0,~\text{for any nonnegative integer}~ i.$ Using the representation, we give a new additive result of the generalized Drazin inverse for two bounded linear operators $P,Q \in \mathbf{B}(X)$ with $PQ^{d}=0$ and $PQ^{i}P=0$, for any integer $i\geq 1$. As corollaries, several well-known results are generalized.

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Bu Makaleye Atıf Yap

Guo, L., Zou, H., Chen, J. (2020). The generalized Drazin inverse of operator matrices. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 3. https://doi.org/10.15672/hujms.731518

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