• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.543-554
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• 2005

In this paper it is proved that for p-hyponormal or log-hyponormal operator A there exist an associated hyponormal operator T, a quasi-affinity X and an injection operator Y such that TX = XA and AY = YT. The operator A and T have the same spectral picture. We apply these results to give brief proofs of some well known spectral properties of p-hyponormal and log­hyponormal operators, amongst them that the spectrum is a con­tinuous function on these classes of operators.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.37-48
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• 2003

In this paper, we show that for a pure hyponormal operator the analytic spectral subspace and the algebraic spectral subspace are coincide. Using this result, we have the following result: Let T be a decomposable operator on a Banach space X and let S be a pure hyponormal operator on a Hilbert space H. Then every linear operator ${\theta}:X{\rightarrow}H$ with $S{\theta}={\theta}T$ is automatically continuous.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.233-246
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• 2016

In this paper, we introduce the class of analytic extensions of M-hyponormal operators and we study various properties of this class. We also use a special Sobolev space to show that every analytic extension of an M-hyponormal operator T is subscalar of order 2k + 2. Finally we obtain that an analytic extension of an M-hyponormal operator satisfies Weyl's theorem.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.21-27
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• 1998

In this paper we prove a structure theorem for p-hyponomal contractions and also give an example of a p-hyponormal operator which is not *-paranormal.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.235-241
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• 2001

In this paper we study some properties of he joint Weyl and Browder spectra for the slightly larger classes containing doubly commuting n-tuples of hyponormal operators.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.571-577
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• 2005

In this paper we prove that if T is a k-th root of a p­hyponormal operator when T is compact or T$^{n}$ is normal for some integer n > k, then T is (generalized) scalar, and that if T is a k-th root of a semi-hyponormal operator and have the property $\sigma$(T) is contained in an angle < 2$\pi$/k with vertex in the origin, then T is subscalar.

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.273-277
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• 2003

The Fuglede-Putnam Theorem is that if A and B are normal operators and X is an operator such that AX = XB, then $A^{\ast}= X. In this paper, we show that if A is $\omega$-hyponormal and $B^{\ast}$ is invertible $\omega$-hyponormal such that AX = XB for a Hilbert-Schmidt operator X, then $A^{\ast}X = XB^{\ast}$.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.747-753
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• 2006

We say operators A, B on Hilbert space satisfy Fuglede-Putnam theorem if AX = X B for some X implies $A^*X=XB^*$. We show that if either (1) A is p-hyponormal and $B^*$ is a class y operator or (2) A is a class y operator and $B^*$ is p-hyponormal, then A, B satisfy Fuglede-Putnam theorem.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.553-563
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• 2006

Let A be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of A is the set ${\sigma}_{B{\omega}}(A)$ of all ${\lambda}{\in}\mathbb{C}$ such that $A-{\lambda}I$ is not a B-Fredholm operator of index 0. Let E(A) be the set of all isolated eigenvalues of A. Recently in [6] Berkani showed that if A is a hyponormal operator, then A satisfies generalized Weyl's theorem ${\sigma}_{B{\omega}}(A)={\sigma}(A)$\E(A), and the B-Weyl spectrum ${\sigma}_{B{\omega}}(A)$ of A satisfies the spectral mapping theorem. In [51], H. Weyl proved that weyl's theorem holds for hermitian operators. Weyl's theorem has been extended from hermitian operators to hyponormal and Toeplitz operators [12], and to several classes of operators including semi-normal operators ([9], [10]). Recently W. Y. Lee [35] showed that Weyl's theorem holds for algebraically hyponormal operators. R. Curto and Y. M. Han [14] have extended Lee's results to algebraically paranormal operators. In [19] the authors showed that Weyl's theorem holds for algebraically p-hyponormal operators. As Berkani has shown in [5], if the generalized Weyl's theorem holds for A, then so does Weyl's theorem. In this paper all the above results are generalized by proving that generalizedWeyl's theorem holds for the case where A is an algebraically ($p,\;k$)-quasihyponormal or an algebarically paranormal operator which includes all the above mentioned operators.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.793-803
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• 2010

In this note, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on $L^2(\cal{F})$ such as, p-quasihyponormal, p-paranormal, p-hyponormal and weakly hyponormal. Some examples are then presented to illustrate that weighted composition operators lie between these classes.