New additive results for the generalized Drazin inverse in a Banach algebra

Ela Some Additive Results for the Generalized Drazin Inverse in a Banach Algebra

In this note, additive results are presented for the generalized Drazin inverse in Banach algebra. Necessary and sufficient conditions are given for the generalized Drazin invertibility of the sum of two commuting generalized Drazin invertible elements. These results are a generalization of the results from the paper [C.Y. Deng and Y. Wei. New additive results for the generalized Drazin inverse...

Some additive results for the generalized Drazin inverse in a Banach algebra

Additive results for the generalized Drazin inverse in a Banach algebra

In this paper we investigate additive properties of the generalized Drazin inverse in a Banach algebra. We find some new conditions under which the generalized Drazin inverse of the sum a + b could be explicitly expressed in terms of a, a, b, b. Also, some recent results of Castro and Koliha (Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), 1085-1097) are extended. 2000 Mathematics Subject Classif...

Generalized Drazin inverse of certain block matrices in Banach algebras

Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.  

Expressions for the generalized Drazin inverse of a block matrix in a Banach algebra

We present some new representations for the generalized Drazin inverse of a block matrix with generalized Schur complement being generalized Drazin invertible in a Banach algebra under conditions weaker than those used in recent papers on the subject.