A perturbed elementary operator and range-kernel orthogonality期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A perturbed elementary operator and range-kernel orthogonality

Authors:	B. P. Duggal

Affiliation:	Department of Mathematics, College of Science UAEU, P.O. Box 17551, Al Ain, United Arab Emirates

Abstract:	Let denote the algebra of operators on a Hilbert . If and $B_jin B(mathcal{H})$ are commuting normal operators, and and $D_jin B(mathcal{H})$ are commuting quasi-nilpotents such that , then define $M_j, N_jin B(mathcal{H})$ and by , , ${mathcal E}(X)=A_1XA_2+B_1XB_2$ and . It is proved that $E^{-1}(0)subseteq H_0({mathcal E})={mathcal E}^{-1}(0)$ and $Xin E^{-1}(0)Longrightarrow vertvert Xvertvertleq k textrm{dist}(X, {mathcal E}(B(mathcal{H})))$ , where is some scalar and $H_0({mathcal E})$ is the quasi-nilpotent part of the operator .

Keywords:	Hilbert space elementary operator normal operator quasi-nilpotent operator generalized scalar operator orthogonality

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