• Title, Summary, Keyword: Toeplitz operators

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TOEPLITZ OPERATORS ON HARDY AND BERGMAN SPACES OVER BOUNDED DOMAINS IN THE PLANE

  • Chung, Young-Bok;Na, Heui-Geong
    • Honam Mathematical Journal
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    • v.39 no.2
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    • pp.143-159
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    • 2017
  • In this paper, we show that algebraic properties of Toeplitz operators on both Bergman spaces and Hardy spaces on the unit disc essentially generalizes on arbitrary bounded domains in the plane. In particular, we obtain results for the uniqueness property and commuting problems of the Toeplitz operators on the Hardy and the Bergman spaces associated to bounded domains.

HYPONORMAL TOEPLITZ OPERATORS ON THE BERGMAN SPACE. II.

  • Hwang, In-Sung;Lee, Jong-Rak
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.3
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    • pp.517-522
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    • 2007
  • In this paper we consider the hyponormality of Toeplitz operators $T_\varphi$ on the Bergman space $L_\alpha^2(\mathbb{D})$ with symbol in the case of function $f+\bar{g}$ with polynomials f and g. We present some necessary conditions for the hyponormality of $T_\varphi$ under certain assumptions about the coefficients of $\varphi$.

HYPONORMALITY OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

  • Hwang, In-Sung
    • Journal of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.1027-1041
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    • 2008
  • In this paper we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Bergman space $L_a^2{(\mathbb{D})$ in the cases, where ${\varphi}\;:=f+\bar{g}$ (f and g are polynomials). We present some necessary or sufficient conditions for the hyponormality of $T_{\varphi}$ under certain assumptions about the coefficients of ${\varphi}$.

HYPONORMAL TOEPLITZ OPERATORS ON THE BERGMAN SPACE

  • Lee, Jong-Rak;Lee, You-Ho
    • Honam Mathematical Journal
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    • v.30 no.1
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    • pp.127-135
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    • 2008
  • In this paper we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Bergman space $L^2_a(\mathbb{D})$ with symbol in the case of function f + $\overline{g}$ with polynomials f and g. We present some necessary conditions for the hyponormality of $T_{\varphi}$, under certain assumptions about the coefficients of ${\varphi}$.

COMPACT TOEPLITZ OPERATORS

  • Kang, Si Ho
    • Honam Mathematical Journal
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    • v.35 no.3
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    • pp.343-350
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    • 2013
  • In this paper we prove that if Toeplitz operators $T^{\alpha}_u$ with symbols in RW satisfy ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}{\rightarrow}0$ as $z{\rightarrow}{\partial}\mathbb{D}$ then $T^{\alpha}_u$ is compact and also prove that if $T^{\alpha}_u$ is compact then the Berezin transform of $T^{\alpha}_u$ equals to zero on ${\partial}\mathbb{D}$.

TOEPLITZ OPERATORS ON GENERALIZED FOCK SPACES

  • Cho, Hong Rae
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.3
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    • pp.711-722
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    • 2016
  • We study Toeplitz operators $T_{\nu}$ on generalized Fock spaces $F^2_{\phi}$ with a locally finite positive Borel measures ${\nu}$ as symbols. We characterize operator-theoretic properties (boundedness and compactness) of $T_{\nu}$ in terms of the Fock-Carleson measure and the Berezin transform ${\tilde{\nu}}$.

ON HYPONORMALITY OF TOEPLITZ OPERATORS WITH POLYNOMIAL AND SYMMETRIC TYPE SYMBOLS

  • Hazarika, Munmun;Phukon, Ambeswar
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.3
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    • pp.617-625
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    • 2011
  • In [6], it was shown that hyponormality for Toeplitz operators with polynomial symbols can be reduced to classical Schur's algorithm in function theory. In [6], Zhu has also given the explicit values of the Schur's functions ${\Phi}_0$, ${\Phi}_1$ and ${\Phi}_2$. Here we explicitly evaluate the Schur's function ${\Phi}_3$. Using this value we find necessary and sufficient conditions under which the Toeplitz operator $T_{\varphi}$ is hyponormal, where ${\varphi}$ is a trigonometric polynomial given by ${\varphi}(z)$ = ${\sum}^N_{n=-N}a_nz_n(N{\geq}4)$ and satisfies the condition $\bar{a}_N\(\array{a_{-1}\\a_{-2}\\a_{-4}\\{\vdots}\\a_{-N}}\)=a_{-N}\;\(\array{\bar{a}_1\\\bar{a}_2\\\bar{a}_4\\{\vdots}\\\bar{a}_N}\)$. Finally we illustrate the easy applicability of the derived results with a few examples.

RANGE INCLUSION OF TWO SAME TYPE CONCRETE OPERATORS

  • Nakazi, Takahiko
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.6
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    • pp.1823-1830
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    • 2016
  • Let H and K be two Hilbert spaces, and let A and B be two bounded linear operators from H to K. We are interested in $RangeB^*{\supseteq}RangeA^*$. It is well known that this is equivalent to the inequality $A^*A{\geq}{\varepsilon}B^*B$ for a positive constant ${\varepsilon}$. We study conditions in terms of symbols when A and B are singular integral operators, Hankel operators or Toeplitz operators, etc.

ON A CLASS OF REFLEXIVE TOEPLITZ OPERATORS

  • HEDAYATIAN, K.
    • Honam Mathematical Journal
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    • v.28 no.4
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    • pp.543-547
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    • 2006
  • We will use a result of Farrell, Rubel and Shields to give sufficient conditions under which a Toeplitz operator with conjugate analytic symbol to be reflexive on Dirichlet-type spaces.

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