• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.899-910
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• 2016

It is known that a semi-cubically hyponormal weighted shift need not satisfy the flatness property, in which equality of two weights forces all or almost all weights to be equal. So it is a natural question to describe all semi-cubically hyponormal weighted shifts $W_{\alpha}$ with first two weights equal. Let ${\alpha}$ : 1, 1, ${\sqrt{x}}$(${\sqrt{u}}$, ${\sqrt{v}}$, ${\sqrt{w}}$)^ be a backward 3-step extension of a recursively generated weight sequence with 1 < x < u < v < w and let $W_{\alpha}$ be the associated weighted shift. In this paper we characterize completely the semi-cubical hyponormal $W_{\alpha}$ satisfying the additional assumption of the positive determinant coefficient property, which result is parallel to results for quadratic hyponormality.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.579-590
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• 2020

The flatness property of a unilateral weighted shifts is important to study the gaps between subnormality and hyponormality. In this paper, we first summerize the results on the flatness for some special kinds of a weighted shifts. And then, we consider the flatness property for a local-cubically hyponormal weighted shifts, which was introduced in [2]. Let α : ${\sqrt{\frac{2}{3}}}$, ${\sqrt{\frac{2}{3}}}$, $\{{\sqrt{\frac{n+1}{n+2}}}\}^{\infty}_{n=2}$ and let W_α be the associated weighted shift. We prove that W_α is a local-cubically hyponormal weighted shift W_α of order ${\theta}={\frac{\pi}{4}}$ by numerical calculation.

• 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.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.855-861
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• 2007

Let A and B be commuting bounded linear operators on a Hilbert space. In this paper, we study spectral area estimates for norms of $A^*B-BA^*$ when A is subnormal or p-hyponormal.

• 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.

• 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 Korean Mathematical Society
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• v.42 no.2
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• pp.387-403
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• 2005

In this note we consider the hyponormality of Toeplitz operators $B_\varphi$ on the Bergman space $L_a^2$ (D) with symbol in the class of functions f + g with polynomials f and g

• 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.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.53-62
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• 2000

In this paper we explore relations between joint Weyl and Browder spectra. Also, we give a spectral characterization of the Taylor-Browder spectrum for special classes of doubly commuting n-tuples of operators and then give a partial answer to Duggal's question.

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.217-223
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• 2003

Let $\cal{K}$ be the extension Hilbert space of a Hilbert space $\cal{H}$ and let $\Phi$ be the faithful $\ast$-representation of $\cal{B}(\cal{H})$ on $\cal{k}$. In this paper, we show that if T is an irreducible ${\omega}-hyponormal$ operators such that $ker(T)\;{\subset}\;ker(T^{*})$ and $T^{*}T\;-\;TT^{\ast}$ is compact, then $\sigma_{e}(T)\;=\;\sigma_{e}(\Phi(T))$.