• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1337-1346
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• 2015

We examine the relationship of the shape operator of a surface of Euclidean 3-space with its Gauss map of pointwise 1-type. Surfaces with constant mean curvature and right circular cones with respect to some properties of the shape operator are characterized when their Gauss map is of pointwise 1-type.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.537-545
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• 2012

In the present paper, we show that a continuous linear operator T on a Frechet space satisfies the Hypercyclic Criterion with respect to a syndetic sequence must satisfy the Kitai Criterion. On the other hand, an operator, hereditarily hypercyclic with respect to a syndetic sequence must be mixing. We also construct weighted shift operators satisfying the Hypercyclicity Criterion which do not satisfy the Kitai Criterion. In other words, hereditarily hypercyclic operators without being mixing.

• 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.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.315-323
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• 2018

In this study, firstly we introduce generalized differential and integral operator, also using integral operator two classes are presented. Furthermore, some subordination results involving the Hadamard product (Convolution) for these subclasses of analytic function are proved. A number of consequences of some of these subordination results are also discussed.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.113-119
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• 2011

Let T be a bounded linear operator on a complex Hilbert space $\mathcal{H}$. An operator T is called class A operator if ${\left|{T^2}\right|}{\geq}{\left|{T^2}\right|}$ and is called class A(k) operator if $({T^*\left|T\right|^{2k}T})^{\frac{1}{k+1}}{\geq}{\left|T\right|}^2$. In this paper, we show that ${\sigma}$ is continuous when restricted to the set of class A operators and consider the tensor products of class A(k) operators.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.645-655
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• 2019

In this article, we show that the nuclear operator defined on Banach space has an extending and lifting operator. Also we give new proofs of the well known facts which were given $Pelcz{\acute{y}}nski$ theorem for complemented subspaces of ${\ell}_1$ and Lewis and Stegall's theorem for complemented subspaces of $L_1({\mu})$.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.1-10
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• 2023

Criteria for an algebraic operator T on a complex Hilbert space 𝓗 to be unitary are established. The main one is written in terms of the convergence of sequences of the form {||Tⁿh||}^∞_n=0 with h ∈ 𝓗. Related questions are also discussed.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.6
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• pp.846-852
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• 1986

An efficient and reliable method for the extraction of features is presented. The method utilizes by a state technique with Euclidean distance operator. The proposed method is compared with the Sobel Operator. Simulation results show that our method performs as well as the Sobel operator.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.193-202
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• 2005

We define a general space $H_{{\omega},p}$ of the Hardy space and improve that Aleman's results to the space $H_{{\omega},p}$. It follows that the multiplication operator on this space is cellular indecomposable and that each invariant subspace contains nontrivial bounded functions.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1315-1327
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• 2011

Let M be a real hypersurface of a complex space form with almost contact metric structure (${\phi}$, ${\xi}$, ${\eta}$, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},\;{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when $R_{\xi}{\phi}S=R_{\xi}S{\phi}$ holds on M, where S denotes the Ricci tensor of type (1,1) on M.