Banach代数中广义Drazin逆的相关结果

令a,b均为Banach代数中广义Drazin可逆的元素, a^d为a的广义Drazin逆, a^π=1-aa^d. 用Banach代数中的幂等元给出元素a,b在ab^π=a, b^πba^π=b^πb, b^πa^πa²b=b^πa^πaba, b^πa^πb²a=b^πa^πbab等条件下a+b广义Drazin逆的表达式.

Relevant Results on Generalized DrazinInverses in a Banach Algebra

Let a,b be two generalized Drazin invertible elements in a Banach algebra, a^d be the generalized Drazin inverse of aaⁿd a^π=1-aa^d. We  gave the expressions for the generalized Drazin JP2]inverse of the sum a+b  under some conditions such as ab^π=a, b^πba^π=b^πb, b^πa^πa²b=b^πa^πaba, b^πa^πb²a=b^πa^πbab etc by using the idempotent element in a Banach algebra.