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ISSN : 1226-0657

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Vol.10 No.4
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ESSENTIAL SPECTRA OF w-HYPONORMAL OPERATORS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Kim, Jae-Hee
Lee, Kwang-Il
Cha,, H. , Kim,, J. , & Lee,, K. (2003). ESSENTIAL SPECTRA OF w-HYPONORMAL OPERATORS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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