• 대한수학회지
• /
• 제41권1호
• /
• pp.95-105
• /
• 2004

In this paper we will consider the weighted composition operators W = $uC_{\tau}$ between $L^{p}$$(X,\sum,\mu$) spaces and Orlicz spaces $L^{\phi}$$(X,\sum,\mu$) generated by measurable and non-singular transformations $\tau$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\tau$ that induce weighted composition operators between $L^{p}$ -spaces by using some properties of conditional expectation operator, pair (u,${\gamma}$) and the measure space $(X,\sum,\mu$). Also, some other properties of these types of operators will be investigated.

• 대한수학회논문집
• /
• 제33권4호
• /
• pp.1125-1140
• /
• 2018

Let A be a normed space, ${\mathcal{B}}(A)$ the algebra of all bounded operators on A, and V a family of strongly upper semicontinuous functions from a Hausdorff completely regular space X into ${\mathcal{B}}(A)$. In this paper, we investigate some properties of the weighted spaces CV (X, A) of all A-valued continuous functions f on X such that the mapping $x{\mapsto}v(x)(f(x))$ is bounded on X, for every $v{\in}V$, endowed with the topology generated by the seminorms ${\parallel}f{\parallel}v={\sup}\{{\parallel}v(x)(f(x)){\parallel},\;x{\in}X\}$. Our main purpose is to characterize continuous, bounded, and locally equicontinuous weighted composition operators between such spaces.

• 대한수학회논문집
• /
• 제38권4호
• /
• pp.1075-1090
• /
• 2023

In this paper, we study new classes of operators k-quasi (m, n)-paranormal operator, k-quasi (m, n)^*-paranormal operator, k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬^* operator which are the generalization of (m, n)-paranormal and (m, n)^*-paranormal operators. We give matrix characterizations for k-quasi (m, n)-paranormal and k-quasi (m, n)^*-paranormal operators. Also we study some properties of k-quasi (m, n)-class 𝒬 operator and k-quasi (m, n)-class 𝒬^* operators. Moreover, these classes of composition operators on L² spaces are characterized.

• 대한수학회지
• /
• 제54권2호
• /
• pp.627-645
• /
• 2017

In this paper, we characterize the boundedness, compactness and essential norm of products of differentiation and composition operators from the Bloch space and weighted Dirichlet spaces to analytic Morrey type spaces.

• 대한수학회보
• /
• 제48권6호
• /
• pp.1119-1124
• /
• 2011

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

• 대한수학회보
• /
• 제51권4호
• /
• pp.1187-1193
• /
• 2014

We will characterize the boundedness and compactness of weighted composition operators on the minimal M$\ddot{o}$bius invariant space.

• Kyungpook Mathematical Journal
• /
• 제56권1호
• /
• pp.125-130
• /
• 2016

A finite rank difference of two composition operators is studied on a Hilbert Lebesgue space or a Hilbert Hardy space.

• 대한수학회지
• /
• 제48권5호
• /
• pp.969-984
• /
• 2011

This paper discusses the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on the open unit ball $B_N$ of $\mathbb{C}^N$. Several analytic properties of linear fractional self-maps of $B_N$ are given. According to these properties, a few necessary conditions for a weighted composition operator to be hypercyclic in the space of holomorphic functions are proved. Besides, the hypercyclicity of adjoint of weighted composition operators are studied in this paper.

• 한국수학사학회지
• /
• 제33권5호
• /
• pp.277-287
• /
• 2020

There are many results for Zadeh's max-min composition operators based on Zadeh's extension principle. We calculate Zadeh's max-min composition operators for two triangular fuzzy numbers defined on ℝ.

• Kyungpook Mathematical Journal
• /
• 제49권4호
• /
• pp.683-689
• /
• 2009

We investigate the gaps among classes of weakly hyponormal composition operators induced by Embry characterization for the subnormality. The relationship between subnormality and weak hyponormality will be discussed in a version of composition operator induced by a non-singular measurable transformation.