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ISSN : 1226-0657

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Vol.2 No.2
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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
1995, v.2 no.2, pp.91-95
Lee, Moo-Sang
Lee,, M. (1995). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 2(2), 91-95.
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Abstract

Let H be an arbitrary complex Hilbert space and let (equation omitted)(H) be the *-algebra of all bounded linear operators on H. An operator T in (equation omitted)(H) is called normal if T<TEX>$\^$</TEX>＊/T = TT<TEX>$\^$</TEX>＊/, hyponormal if T<TEX>$\^$</TEX>＊/T <TEX>$\geq$</TEX> TT<TEX>$\^$</TEX>＊/, and quasi-hyponormal if T<TEX>$\^$</TEX>＊/(T<TEX>$\^$</TEX>＊/T － TT<TEX>$\^$</TEX>＊/)A <TEX>$\geq$</TEX> 0, or equivalently ∥T<TEX>$\^$</TEX>＊/T<TEX>$\chi$</TEX>∥ <TEX>$\leq$</TEX> ∥TT<TEX>$\chi$</TEX>∥ for all <TEX>$\chi$</TEX> in H.(omitted)

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

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