A NOTE ON QUASI-SIMILAR QUASI-HYPONORMAL OPERATORS

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$\^$＊/T = TT$\^$＊/, hyponormal if T$\^$＊/T $\geq$ TT$\^$＊/, and quasi-hyponormal if T$\^$＊/(T$\^$＊/T － TT$\^$＊/)A $\geq$ 0, or equivalently ∥T$\^$＊/T$\chi$∥ $\leq$ ∥TT$\chi$∥ for all $\chi$ in H.(omitted)