• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.1
• /
• pp.65-73
• /
• 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 ${\varphi}$.

• Honam Mathematical Journal
• /
• v.40 no.1
• /
• pp.155-162
• /
• 2018

In this paper, we are concerned with hyponormal Toeplitz operators on the Hardy space of the unit circle. Our main result of this paper is to provide a simple and transparent proof on the hyponormality of Toeplitz operators with symmetric-type symbols via Schur complement lemma.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1421-1441
• /
• 2017

We compute explicitly the matrix represented by the Toeplitz operator on the Hardy space over a smoothly finitely connected bounded domain in the plane with respect to special orthonormal bases consisting of the classical kernel functions for the space of square integrable functions and for the Hardy space. The Fourier coefficients of the symbol of the Toeplitz operator are obtained from zeroth row vectors and zeroth column vectors of the matrix. And we also find some condition for the product of two Toeplitz operators to be a Toeplitz operator in terms of matrices.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.647-653
• /
• 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
• /
• v.29 no.2
• /
• pp.257-262
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.437-450
• /
• 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
• /
• v.36 no.2
• /
• pp.357-361
• /
• 1999

The essential spectra for a class of Toeplitz operators on p, 1$\leq$p$\leq$$\infty$, are computed.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.319-331
• /
• 2019

On the weighted Dirichlet space, by the Sobolev's embedding theorem, we characterize the compactness for operators which are finite sums of products of several Toeplitz operators. Moreover, the essential spectrum of Toeplitz operator is characterized.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.161-170
• /
• 2023

We consider dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space on the unit disk. We give a characterization of when a finite sum of products of two dual Toeplitz operators is equal to 0. Our result extends several known results by using a unified way.

• Journal of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.259-269
• /
• 2006

We obtain a characterization of commuting Toeplitz operators with holomorphic symbols acting on the pluriharmonic Bergman space of the polydisk. We also obtain a characterization of normal Toeplitz operators with pluriharmonic symbols. In addition, some results for special types of semi-commutators are included.