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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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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: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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, 10(4), 217-223.

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

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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