2006•Journal of Inequalities and ApplicationsOpen access

Essential spectra of quasisimilar (p,k)-quasihyponormal operators

An-Hyun Kim, In Hyoun Kim

Abstract

It is shown that if is an upper-triangular operator matrix acting on the Hilbert space and if denotes the essential spectrum, then the passage from to is accomplished by removing certain open subsets of from the former. Using this result we establish that quasisimilar -quasihyponormal operators have equal spectra and essential spectra.

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Key concepts: Essential spectrum, Hilbert space, Spectrum (functional analysis), Operator matrix, Spectral line, Mathematics, Triangular matrix, Operator (biology)