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ISSN : 1226-0657

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Vol.5 No.2
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ON p-HYPONORMAL OPERATORS ON A HILBERT SPACE

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1998, v.5 no.2, pp.109-114
Cha, Hyung-Koo (Department of Mathematics, Hanyang University)
Cha, Hyung-Koo. (1998). ON p-HYPONORMAL OPERATORS ON A HILBERT SPACE. 한국수학교육학회지시리즈B:순수및응용수학, 5(2), 109-114.
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Abstract

Let H be a separable complex H be a space and let (equation omitted)(H) be the *-algebra of all bounded linear operators on H. An operator T in (equation omitted)(H) is said to be p-hyponormal if (<TEX>$T^{\ast}T)^p - (TT^{\ast})^{p}\geq$</TEX> 0 for 0 ＜ p ＜ 1. If p = 1, T is hyponormal and if p = <TEX>$\frac{1}{2}$</TEX>, T is semi-hyponormal. In this paper, by using a technique introduced by S. K. Berberian, we show that the approximate point spectrum <TEX>$\sigma_{\alpha p}(T) of a pure p-hyponormal operator T is empty, and obtains the compact perturbation of T.

keywords
polar decomposition, p-hyponormal, spectrum, approximate point spectrum, joint point spectrum, joint approximate point spectrum, trace norm, strongly normal

한국수학교육학회지시리즈B:순수및응용수학

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