Theoretical Mathematics and Pedagogical Mathematics (한국수학교육학회지시리즈B:이론수학과 교직수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지

ESSENTIAL SPECTRA OF ${\omega}-HYPONORMAL$ OPERATORS

  • Published : 2003.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

Let $\cal{K}$ be the extension Hilbert space of a Hilbert space $\cal{H}$ and let $\Phi$ be the faithful $\ast$-representation of $\cal{B}(\cal{H})$ on $\cal{k}$. In this paper, we show that if T is an irreducible ${\omega}-hyponormal$ operators such that $ker(T)\;{\subset}\;ker(T^{*})$ and $T^{*}T\;-\;TT^{\ast}$ is compact, then $\sigma_{e}(T)\;=\;\sigma_{e}(\Phi(T))$.

Keywords