The generalized Drazin inverse of operator matrices

Li GUO; Honglin ZOU; Jianlong CHEN

doi:https://doi.org/10.15672/hujms.731518

Makale detayları

The generalized Drazin inverse of operator matrices

Yazarlar:

Li GUO | Honglin ZOU | Jianlong CHEN

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 3, pp.1134-1149

Belge Tipi:

Makale

Yayın Tarihi:

6/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000451101

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.731518

Özet:

 

Representations for the generalized Drazin inverse of an operator matrix (ABCD)(ABCD)\begin{pmatrix}A & B \\ C & D \end{pmatrix} are presented in terms of  A,B,C,DA,B,C,DA,B,C,D and the generalized Drazin inverses of A,DA,DA,D, under the condition that BDd=0, and BDiC=0, for any nonnegative integer i.BDd=0, and BDiC=0, for any nonnegative integer i.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∈B(X)P,Q∈B(X)P,Q \in \mathbf{B}(X) with PQd=0PQd=0PQ^{d}=0 and PQiP=0PQiP=0PQ^{i}P=0, for any  integer i≥1i≥1i\geq 1. As corollaries, several well-known results are generalized.

Makale detayları

The generalized Drazin inverse of operator matrices

Yazarlar: Li GUO | Honglin ZOU | Jianlong CHEN

Yayıncı: Hacettepe University

Ana Başlıklar: Matematik

Dergi: Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 3, pp.1134-1149

Belge Tipi: Makale

Yayın Tarihi: 6/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000451101

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

DOI: https://doi.org/10.15672/hujms.731518

Sayı

Yazarlar:

Li GUO | Honglin ZOU | Jianlong CHEN

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 3, pp.1134-1149

Belge Tipi:

Makale

Yayın Tarihi:

6/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000451101

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.731518