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

Copyright © 2006 An-Hyun Kim and In Hyoun Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.