• Title/Summary/Keyword: Toeplitz operators

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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.

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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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 $L^2_a(\mathbb{D},\mathbb{C}^n)$.

THE TOEPLITZ OPERATOR INDUCED BY AN R-LATTICE

  • Kang, Si Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.3
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    • pp.491-499
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    • 2012
  • The hyperbolic metric is invariant under the action of M$\ddot{o}$bius maps and unbounded. For 0 < $r$ < 1, there is an r-lattice in the Bergman metric. Using this r-lattice, we get the measure ${\mu}_r$ and the Toeplitz operator $T^{\alpha}_{\mu}_r$ and we prove that $T^{\alpha}_{\mu}_r$ is bounded and $T^{\alpha}_{\mu}_r$ is compact under some condition.

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.

REDUCING SUBSPACES FOR TOEPLITZ OPERATORS ON THE POLYDISK

  • Shi, Yanyue;Lu, Yufeng
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.2
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    • pp.687-696
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    • 2013
  • In this note, we completely characterize the reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on $A^2_{\alpha}(D^2)$ where ${\alpha}$ > -1 and N, M are positive integers with $N{\neq}M$, and show that the minimal reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on the unweighted Bergman space and on the weighted Bergman space are different.