ESSENTIAL SPECTRA OF w-HYPONORMAL OPERATORS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2003, v.10 no.4, pp.217-223

Cha, Hyung-Koo (Department of Mathematics, Hanyang University)
Kim, Jae-Hee (Department of Mathematics, Hanyang University)
Lee, Kwang-Il (Department of Mathematics, Hanyang University)

Cha, Hyung-Koo, Kim, Jae-Hee, & Lee, Kwang-Il. (2003). ESSENTIAL SPECTRA OF <TEX>${\omega}-HYPONORMAL$</TEX> OPERATORS. 한국수학교육학회지시리즈B:순수및응용수학, 10(4), 217-223.

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Abstract

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

keywords: <tex> {\omega}-hyponormal$</tex>, approximate point spectrum, essential spectrum, irreducible operator

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논문 상세

Vol.10 No.4

ESSENTIAL SPECTRA OF <TEX>${\omega}-HYPONORMAL$</TEX> OPERATORS

ESSENTIAL SPECTRA OF w-HYPONORMAL OPERATORS

Abstract

한국수학교육학회지시리즈B:순수및응용수학