• Title, Summary, Keyword: Toeplitz operators

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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.

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.

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.

TRUNCATED HANKEL OPERATORS AND THEIR MATRICES

  • Lanucha, Bartosz;Michalska, Malgorzata
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.187-200
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    • 2019
  • Truncated Hankel operators are compressions of classical Hankel operators to model spaces. In this paper we describe matrix representations of truncated Hankel operators on finite-dimensional model spaces. We then show that the obtained descriptions hold also for some infinite-dimensional cases.

THE HYPONORMAL TOEPLITZ OPERATORS ON THE VECTOR VALUED BERGMAN SPACE

  • Lu, Yufeng;Cui, Puyu;Shi, Yanyue
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.237-252
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    • 2014
  • In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space $L^2_a(\mathbb{D},\mathbb{C}^n)$. We also show some necessary conditions for the hyponormality of $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.

SEMI-QUASITRIANGULARITY OF TOEPLITZ OPERATORS WITH QUASICONTINUOUS SYMBOLS

  • Kim, In-Hyoun;Lee, Woo-Young
    • Communications of the Korean Mathematical Society
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    • v.13 no.1
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    • pp.77-84
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    • 1998
  • In this note we show that if $T_{\varphi}$ is a Toeplitz operator with quasicontinuous symbol $\varphi$, if $\omega$ is an open set containing the spectrum $\sigma(T_\varphi)$, and if $H(\omega)$ denotes the set of analytic fuctions defined on $\omege$, then the following statements are equivalent: (a) $T_\varphi$ is semi-quasitriangular. (b) Browder's theorem holds for $f(T_\varphi)$ for every $f \in H(\omega)$. (c) Weyl's theorem holds for $f(T_\varphi)$ for every $f \in H(\omega)$. (d) $\sigma(T_{f \circ \varphi}) = f(\sigma(T_varphi))$ for every $f \in H(\omega)$.

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REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON WEIGHTED HARDY SPACES OVER BIDISK

  • Kuwahara, Shuhei
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.4
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    • pp.1221-1228
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    • 2017
  • We consider weighted Hardy spaces on bidisk ${\mathbb{D}}^2$ which generalize the weighted Bergman spaces $A^2_{\alpha}({\mathbb{D}}^2)$. Let z, w be coordinate functions and $T_{{\bar{z}}^N}_w$ Toeplitz operator with symbol $_{{\bar{z}}^N}_w$. In this paper, we study the reducing subspaces of $T_{{\bar{z}}^N}_w$ on the weighted Hardy spaces.