• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.287-292
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• 2004

The operator $A \; {\in} \; L(H_{i})$, the Banach algebra of bounded linear operators on the complex infinite dimensional Hilbert space $\cal H_{i}$, is said to be p-hyponormal if $(A^\ast A)^P \geq (AA^\ast)^p$ for $p\; \in \; (0,1]$. Let (equation omitted) denote the completion of (equation omitted) with respect to some crossnorm. Let $I_{i}$ be the identity operator on $H_{i}$. Letting (equation omitted), where each $A_{i}$ is p-hyponormal, it is proved that the commuting n-tuple T = ($T_1$,..., $T_{n}$) satisfies Bishop's condition ($\beta$) and that if T is Weyl then there exists a non-singular commuting n-tuple S such that T = S + F for some n-tuple F of compact operators.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.647-653
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• 2011

In this note we are concerned with the hyponormality of Toeplitz operators $T_{\phi}$ with polynomial symbols ${\phi}=\bar{g}+f(f,g{\in}H^{\infty}(\mathbb{T}))$ when g divides f.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.287-292
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• 2008

We introduce jointly weak subnormal operators. It is shown that if $T=(T_1,T_2)$ is subnormal then T is weakly subnormal and if f $T=(T_1,T_2)$ is weakly subnormal then T is hyponormal. We discuss the flatness of weak subnormal operators.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.497-502
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• 2006

An asymmetric Fuglede-Putnam theorem for $p$-hyponormal operators and class ($\mathcal{Y}$) is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.109-114
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• 1998

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 ($T^{\ast}T)^p - (TT^{\ast})^{p}\geq$ 0 for 0 ＜ p ＜ 1. If p = 1, T is hyponormal and if p = $\frac{1}{2}$, T is semi-hyponormal. In this paper, by using a technique introduced by S. K. Berberian, we show that the approximate point spectrum $\sigma_{\alpha p}(T) of a pure p-hyponormal operator T is empty, and obtains the compact perturbation of T.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.19-28
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• 1997

Let $H$ and $K$ be separable, complex Hilbert spaces and $L(H, K)$ denote the space of all linear, bounded operators from $H$ to $K$. If $H = K$, we write $L(H)$ in place of $L(H, K)$. An operator $T$ in $L(H)$ is called hyponormal if $TT^* \leq T^*T$, or equivalently, if $\left\$\mid$ T^*h \right\$\mid$ \leq \left\$\mid$ Th \right\$\mid$$ for each h in $H$. In [Pu], M. Putinar constructed a universal functional model for hyponormal operators.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.91-95
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• 1995

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)

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.517-522
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• 2007

In this paper we consider the hyponormality of Toeplitz operators $T_\varphi$ on the Bergman space $L_\alpha^2(\mathbb{D})$ with symbol in the case of function $f+\bar{g}$ with polynomials f and g. We present some necessary conditions for the hyponormality of $T_\varphi$ under certain assumptions about the coefficients of $\varphi$.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.127-135
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• 2008

In this paper we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Bergman space $L^2_a(\mathbb{D})$ with symbol in the case of function f + $\overline{g}$ with polynomials f and g. We present some necessary conditions for the hyponormality of $T_{\varphi}$, under certain assumptions about the coefficients of ${\varphi}$.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.163-168
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• 2010

In this paper it is shown that if [$T^*$,T] is of rank one and ker [$T^*$,T] is invariant for T, then T is quasinormal. Thus, we can know that the hyponormal condition is superfluous in the Morrel's theorem.