本文關(guān)鍵詞： 偽Drazin逆 Jacobson根 Banach代數(shù)　出處：《東南大學(xué)學(xué)報(bào)(自然科學(xué)版)》2017年03期 　論文類型：期刊論文

【摘要】：在條件ab=φ(ba)下,研究了ab與a+b的偽Drazin逆的表達(dá)式.其中,a,b是Banach代數(shù)A中的2個(gè)偽Drazin可逆的元素,φ是A上雙射的centralizer.證明了:若a,b是偽Drazin可逆的且ab=φ(ba),則ab是偽Drazin可逆的且(ab)~懔=b~懔a~懔;a+b是偽Drazin可逆的,當(dāng)且僅當(dāng)aa~懔(a+b)是偽Drazin可逆的,當(dāng)且僅當(dāng)aa~懔(a+b)bb~懔是偽Drazin可逆的.此時(shí),(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，

本文編號(hào)：1466250