• 대한수학회보
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• 제48권1호
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• pp.141-149
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• 2011

We consider the problem to determine when a Toeplitz operator is bounded on weighted Bergman spaces. We show that Toeplitz operators induced by elements of some set are bounded and each element of the set is related with a Carleson measure on the weighted Bergman space.

• Korean Journal of Mathematics
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• 제7권2호
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• pp.271-280
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• 1999

We study Toeplitz operators on the harmonic Bergman Space $b^p(\mathbf{H})$, where $\mathbf{H}$ is the upper half space in $\mathbf{R}(n{\geq}2)$, for 1 < $p$ < ${\infty}$. We give characterizations for the Toeplitz operators with positive symbols to be bounded.

• 대한수학회논문집
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• 제37권1호
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• pp.91-103
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• 2022

In this paper, we introduce Toeplitz operators and Hankel operators with complex Borel measures on the closed unit disk. When a positive measure 𝜇 on (-1, 1) is a Carleson measure, it is known that the corresponding Hankel matrix is bounded and vice versa. We show that for a positive measure 𝜇 on 𝔻, 𝜇 is a Carleson measure if and only if the Toeplitz operator with symbol 𝜇 is a densely defined bounded linear operator. We also study Hankel operators of Hilbert-Schmidt class.

• 대한수학회보
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• 제44권2호
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• pp.281-290
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• 2007

We deal with Bergman functions defined on the half-plane. We study integral operators, and some relationship between Berezin transforms and Toeplitz operators, and also show that some Berezin transforms are Mobius invariant.

• 대한수학회보
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• 제54권6호
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• pp.2013-2027
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• 2017

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

• 대한수학회논문집
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• 제34권2호
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• pp.533-542
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• 2019

We study commutants of Toeplitz operators acting on the Dirichlet space of the unit disk and prove that an operator in the Toeplitz algebra commuting with a Toeplitz operator with a nonconstant polynomial symbol must be a Toeplitz operator with an analytic symbol.

• 대한수학회논문집
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• 제35권4호
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• pp.1185-1192
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• 2020

In this paper, we introduce and investigate multi subspace-hypercyclic operators and prove that multi-hypercyclic operators are multi subspace-hypercyclic. We show that if T is M-hypercyclic or multi M-hypercyclic, then Tⁿ is multi M-hypercyclic for any natural number n and by using this result, make some examples of multi subspace-hypercyclic operators. We prove that multi M-hypercyclic operators have somewhere dense orbits in M. We show that analytic Toeplitz operators can not be multi subspace-hypercyclic. Also, we state a sufficient condition for coanalytic Toeplitz operators to be multi subspace-hypercyclic.

• 대한수학회보
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• 제60권4호
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• pp.957-969
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• 2023

Let j be a nonnegative integer. We define the Toeplitz-type operators T^(j)_a with symbol a ∈ L^∞(C), which are variants of the traditional Toeplitz operators obtained for j = 0. In this paper, we study the boundedness of these operators and characterize their compactness in terms of its Berezin transform.

• 대한수학회논문집
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• 제11권4호
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• pp.937-958
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• 1996

On the setting of product of balls we consider Toeplitz operators, with symbols satisfying a certain condition, on the Bergman space. Norms and essential norms of such operators are estimated by means of certain integral quantities.

• 대한수학회지
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• 제42권2호
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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