• Title/Summary/Keyword: Toeplitz operators

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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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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 ${\tilde{\nu}}$.

THE ATOMIC DECOMPOSITION OF HARMONIC BERGMAN FUNCTIONS, DUALITIES AND TOEPLITZ OPERATORS

  • Lee, Young-Joo
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.263-279
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    • 2009
  • On the setting of the unit ball of ${\mathbb{R}}^n$, we consider a Banach space of harmonic functions motivated by the atomic decomposition in the sense of Coifman and Rochberg [5]. First we identify its dual (resp. predual) space with certain harmonic function space of (resp. vanishing) logarithmic growth. Then we describe these spaces in terms of boundedness and compactness of certain Toeplitz operators.

ON 2-HYPONORMAL TOEPLITZ OPERATORS WITH FINITE RANK SELF-COMMUTATORS

  • Kim, An-Hyun
    • Communications of the Korean Mathematical Society
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    • v.31 no.3
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    • pp.585-590
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    • 2016
  • Suppose $T_{\varphi}$ is a 2-hyponormal Toeplitz operator whose self-commutator has rank $n{\geq}1$. If $H_{\bar{\varphi}}(ker[T^*_{\varphi},T_{\varphi}])$ contains a vector $e_n$ in a canonical orthonormal basis $\{e_k\}_{k{\in}Z_+}$ of $H^2({\mathbb{T}})$, then ${\varphi}$ should be an analytic function of the form ${\varphi}=qh$, where q is a finite Blaschke product of degree at most n and h is an outer function.

SOME PROPERTIES OF TOEPLITZ OPERATORS WITH SYMBOL μ

  • Kang, Si Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.3
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    • pp.471-479
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    • 2010
  • For a complex regular Borel measure ${\mu}$ on ${\Omega}$ which is a subset of ${\mathbb{C}}^k$, where k is a positive integer we define the Toeplitz operator $T_{\mu}$ on a reproducing analytic space which comtains polynomials. Using every symmetric polynomial is a polynomial of elementary polynomials, we show that if $T_{\mu}$ has finite rank then ${\mu}$ is a finite linear combination of point masses.

PROPERTIES OF kth-ORDER (SLANT TOEPLITZ + SLANT HANKEL) OPERATORS ON H2(𝕋)

  • Gupta, Anuradha;Gupta, Bhawna
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.855-866
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    • 2020
  • For two essentially bounded Lebesgue measurable functions 𝜙 and ξ on unit circle 𝕋, we attempt to study properties of operators $S^k_{\mathcal{M}({\phi},{\xi})=S^k_{T_{\phi}}+S^k_{H_{\xi}}$ on H2(𝕋) (k ≥ 2), where $S^k_{T_{\phi}}$ is a kth-order slant Toeplitz operator with symbol 𝜙 and $S^k_{H_{\xi}}$ is a kth-order slant Hankel operator with symbol ξ. The spectral properties of operators Sk𝓜(𝜙,𝜙) (or simply Sk𝓜(𝜙)) are investigated on H2(𝕋). More precisely, it is proved that for k = 2, the Coburn's type theorem holds for Sk𝓜(𝜙). The conditions under which operators Sk𝓜(𝜙) commute are also explored.