Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 72641, 7 pages
doi:10.1155/JIA/2006/72641

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

An-Hyun Kim1 and In Hyoun Kim2

 1Department of Mathematics, Changwon National University, Changwon 641–773, Korea
2Department of Mathematics, Seoul National University, Seoul 151-742, Korea
Received 1 July 2005; Accepted 20 September 2005

Abstract

It is shown that if MC=(AC0B) is an 2×2 upper-triangular operator matrix acting on the Hilbert space ℋ⊕𝒦 and if σe(⋅) denotes the essential spectrum, then the passage from σe(A)∪σe(B) to σe(MC) is accomplished by removing certain open subsets of σe(A)∩σe(B) from the former. Using this result we establish that quasisimilar (p,k)-quasihyponormal operators have equal spectra and essential spectra.