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2006•Journal of Mathematical Research and ExpositionRequires access

Quasisimilarity of Operators and Properties of the Essential Spectrum

SU Wei-gang

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Abstract

Let A and B be quasisimilar operators.By means of the analysis of the precise constitution of spectrum of operators,this paper gives the intersection relations between the components of the Wolf essential spectrum,the Kato essential spectrum,the Weyl essential spectrum,the right essential spectrum of operator A and some subsets of the Wolf essential spectrum of operator B,and positively answers the question of L.A.Fialkow in[3].

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What this paper is about

Let A and B be quasisimilar operators.By means of the analysis of the precise constitution of spectrum of operators,this paper gives the intersection relations between the components of the Wolf essential spectrum,the Kato essential spectrum,the Weyl essential spectrum,the right essential spectrum of operator A and some subsets of the Wolf essential spectrum of operator B,and positively answers the question of L.A.Fialkow in[3].

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Available abstract

Let A and B be quasisimilar operators.By means of the analysis of the precise constitution of spectrum of operators,this paper gives the intersection relations between the components of the Wolf essential spectrum,the Kato essential spectrum,the Weyl essential spectrum,the right essential spectrum of operator A and some subsets of the Wolf essential spectrum of operator B,and positively answers the question of L.A.Fialkow in[3].

Key concepts: Essential spectrum, Spectrum (functional analysis), Mathematics, Operator (biology), Intersection (aeronautics), Algebra over a field, Pure mathematics, Discrete mathematics

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