关于Banach代数中伪Drazin逆的进一步结果

发布时间：2018-01-26 18:07

  本文关键词： 伪Drazin逆 Jacobson根 Banach代数　出处：《东南大学学报(自然科学版)》2017年03期 　论文类型：期刊论文

【摘要】：在条件ab=φ(ba)下,研究了ab与a+b的伪Drazin逆的表达式.其中,a,b是Banach代数A中的2个伪Drazin可逆的元素,φ是A上双射的centralizer.证明了:若a,b是伪Drazin可逆的且ab=φ(ba),则ab是伪Drazin可逆的且(ab)~懔=b~懔a~懔;a+b是伪Drazin可逆的,当且仅当aa~懔(a+b)是伪Drazin可逆的,当且仅当aa~懔(a+b)bb~懔是伪Drazin可逆的.此时,(a+b)~懔=(aa~懔(a+b))~懔+sum from n=0 to ∞φ-(n(n+1))/2(1)(b~懔)~(n+1)(-a)~n(1-aa~懔).
[Abstract]:In this paper, we study the expression of the pseudo Drazin inverse of ab and ab under the condition of abb = 蠁 ba. where Drazin b is two elements of Banach algebra A that are pseudo Drazin invertible. 蠁 is a centralizerof bijection on A. It is proved that if a Drazin is pseudo Drazin invertible and abb = 蠁 ba.). Ab is pseudo-#en0# reversible and apprehensive about b ~ apprehensive; A b is pseudo Drazin reversible if and only if a a b is pseudo Drazin reversible. If and only if aa.com apprehensive is pseudo-#en0# reversible. Sum from nu 0 to 鈭，

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