A NOTE ON QUASI-SIMILAR QUASI-HYPONORMAL OPERATORS

Lee, Moo-Sang; Lee, Moo-Sang

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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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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Article Contents

Vol.2 No.2

Abstract

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