• Bulletin of the Korean Mathematical Society
• /
• v.48 no.6
• /
• pp.1119-1124
• /
• 2011

In the present paper, we study the chaotic property of weighted composition operators acting on the holomorphic function space $H(\mathbb{U})$.

• Communications of the Korean Mathematical Society
• /
• v.26 no.4
• /
• pp.591-601
• /
• 2011

In this paper, we deal with the discrete p-Laplacian operators with a potential term having the smallest nonnegative eigenvalue. Such operators are classified as its smallest eigenvalue is positive or zero. We discuss differences between them such as an existence of solutions of p-Laplacian equations on networks and properties of the energy functional. Also, we give some examples of Poisson equations which suggest a difference between linear types and nonlinear types. Finally, we study characteristics of the set of a potential those involving operator has the smallest positive eigenvalue.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.4
• /
• pp.677-686
• /
• 2016

Algebraic spectral subspaces were introduced by Johnson and Sinclair via a transnite sequence of spaces. Laursen simplified the definition of algebraic spectral subspace. Algebraic spectral subspaces are useful in automatic continuity theory of intertwining linear operators on Banach spaces. In this paper, we characterize algebraic spectral subspaces of operators with finite ascent. From this characterization we show that if T is a generalized scalar operator, then T has finite ascent.

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

• Communications of the Korean Mathematical Society
• /
• v.25 no.4
• /
• pp.547-556
• /
• 2010

In this paper, we present the reprentation of all operators B which are Drazin invertible and sharing the spectral projections at 0 with a given Drazin invertible operator A. Meanwhile, some related results for EP operators with closed range are obtained.

• Communications of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.313-325
• /
• 2021

In this paper, we provide a characterization of upper semi-Fredholm operators via the relative demicompactness concept. The obtained results are used to investigate the stability of various essential spectra of closed linear operators under perturbations belonging to classes involving demicompact, as well as, relative demicompact operators.

• Communications of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.717-729
• /
• 2024

Let 𝓑(H) be the algebra of all bounded linear operators on a Hilbert space H with dim(H) > 2. Let 𝒢𝒫(H) be the subset of 𝓑(H) of all generalized projection operators. In this paper, we give a complete characterization of surjective maps 𝚽 : 𝓑(H) → 𝓑(H) satisfying A-𝛌B ∈ 𝒢𝒫(H) ⇔ 𝚽(A) - 𝛌𝚽(B) ∈ 𝒢𝒫(H) for any A, B ∈ 𝓑(H) and 𝛌 ∈ ℂ.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.765-770
• /
• 2000

The object of the present paper is to give an application of a linear operator $L_p(a, c)$ defined by means of a Hadamard product (or convolution) to a Miller and Mocanu’s theorem.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.764-764
• /
• 2000

The object of the present paper is to give an application of a linear operator L(sub)p(a, c) defined by means of a Hadamard product (or convolution) to a Miller and Mocanu’s theorem.

• Journal of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.353-365
• /
• 1994

During the past century, one of the most active and continuing subjects in matrix theory has been the study of those linear operators on matrices that leave certain properties or subsets invariant. Such questions ar usually called "Linear Preserver Problems".