• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.1019-1031
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• 2024

In this paper we consider the sufficient condition for hyponormal Toeplitz operators T_𝛗 with non-harmonic symbols $${\varphi}(z)=\sum_{\ell=1}^{k}{\alpha}_{\ell}z^{{m_{\ell}}{\bar{z}}n_{\ell}}$$ with m_ℓ-n_ℓ = δ > 0 for all 1 ≤ ℓ ≤ k, and α_ℓ ∈ ℂ on the Bergman spaces. In particular, we will observe the characteristics of the hyponormality of the Toeplitz operators T_𝛗 according to the positional relationship of the coefficients α_ℓ's.

• Journal of Digital Contents Society
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• v.10 no.4
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• pp.579-585
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• 2009

In [9], Tyrtshnikov proposed a preconditioned approach to derive a general solution from a Toeplitz linear system. Furthermore, the process of selecting a preconditioner matrix from symmetric Toeplitz matrix, which has been used in previous studies, is introduced. This research introduces a new method for finding the preconditioner in a Toeplitz system. Also, through analyzing these preconditioners, it is derived that eigenvalues of a symmetric Toeplitz are very close to eigenvalues of a new preconditioner for T. It is shown that if the spectrum of the preconditioned system $C_0^{-1}T$ is clustered around 1, then the convergence rate of the preconditioned system is superlinear. From these results, it is determined to get the superliner at the convergence rate by our good preconditioner $C_0$. Moreover, an advantage is driven by increasing various applications i. e. image processing, signal processing, etc. in this study from the proposed preconditioners for Toeplitz matrices. Another characteristic, which this research holds, is that the preconditioner retains the properties of the Toeplitz matrix.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.647-653
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• 2011

In this note we are concerned with the hyponormality of Toeplitz operators $T_{\phi}$ with polynomial symbols ${\phi}=\bar{g}+f(f,g{\in}H^{\infty}(\mathbb{T}))$ when g divides f.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.257-262
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• 2014

In this note we consider "generalized Riesz points" for compact and quasinilpotent perturbations of Toeplitz operators acting on the Hardy space of the unit circle.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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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

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.437-450
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• 2000

On the setting of the half-plane H={x+iy$\mid$y>0} of the complex plane, we study some properties of weighted Bergman spaces and their duality. We also obtain some characterizations of compact Toeplitz operators.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.65-73
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• 2011

In this note we present some necessary and sufficient conditions for the hyponormality of Toeplitz operators $T_{\varphi}$ under certain assumptions concerning the trigonometric polynomial symbol ${\varphi}$.