• Title/Summary/Keyword: Toeplitz operators

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SOME TOEPLITZ OPERATORS AND THEIR DERIVATIVES

  • Kang, Si Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.4
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    • pp.833-842
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    • 2011
  • We prove that Toeplitz operators with symbols in RW are bounded and we calculate some upper bounds of the norm of these Toeplitz operators. We also analyze n-th derivative of Toeplitz operators and get some local estimates.

ON m-ISOMETRIC TOEPLITZ OPERATORS

  • Ko, Eungil;Lee, Jongrak
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.367-378
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    • 2018
  • In this paper, we study m-isometric Toeplitz operators $T_{\varphi}$ with rational symbols. We characterize m-isometric Toeplitz operators $T_{\varphi}$ by properties of the rational symbols ${\varphi}$. In addition, we give a necessary and sufficient condition for Toeplitz operators $T_{\varphi}$ with analytic symbols ${\varphi}$ to be m-expansive or m-contractive. Finally, we give some results for m-expansive and m-contractive Toeplitz operators $T_{\varphi}$ with trigonometric polynomial symbols ${\varphi}$.

H-TOEPLITZ OPERATORS ON THE BERGMAN SPACE

  • Gupta, Anuradha;Singh, Shivam Kumar
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.2
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    • pp.327-347
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    • 2021
  • As an extension to the study of Toeplitz operators on the Bergman space, the notion of H-Toeplitz operators B�� is introduced and studied. Necessary and sufficient conditions under which H-Toeplitz operators become co-isometry and partial isometry are obtained. Some of the invariant subspaces and kernels of H-Toeplitz operators are studied. We have obtained the conditions for the compactness and Fredholmness for H-Toeplitz operators. In particular, it has been shown that a non-zero H-Toeplitz operator can not be a Fredholm operator on the Bergman space. Moreover, we have also discussed the necessary and sufficient conditions for commutativity of H-Toeplitz operators.

TOEPLITZ OPERATORS ON BLOCH-TYPE SPACES AND A GENERALIZATION OF BLOCH-TYPE SPACES

  • Kang, Si Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.3
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    • pp.439-454
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    • 2014
  • We deal with the boundedness of the n-th derivatives of Bloch-type functions and Toeplitz operators and give a relationship between Bloch-type spaces and ranges of Toeplitz operators. Also we prove that the vanishing property of ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}}$ on the boundary of $\mathbb{D}$ implies the compactness of Toeplitz operators and introduce a generalization of Bloch-type spaces.

kth-ORDER ESSENTIALLY SLANT WEIGHTED TOEPLITZ OPERATORS

  • Gupta, Anuradha;Singh, Shivam Kumar
    • Communications of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1229-1243
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    • 2019
  • The notion of $k^{th}$-order essentially slant weighted Toeplitz operator on the weighted Lebesgue space $L^2({\beta})$ is introduced and its algebraic properties are investigated. In addition, the compression of $k^{th}$-order essentially slant weighted Toeplitz operators on the weighted Hardy space $H^2({\beta})$ is also studied.

TOEPLITZ OPERATORS ON HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES

  • Yi, HeungSu
    • Korean Journal of Mathematics
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    • v.7 no.2
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    • pp.271-280
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    • 1999
  • We study Toeplitz operators on the harmonic Bergman Space $b^p(\mathbf{H})$, where $\mathbf{H}$ is the upper half space in $\mathbf{R}(n{\geq}2)$, for 1 < $p$ < ${\infty}$. We give characterizations for the Toeplitz operators with positive symbols to be bounded.

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TOEPLITZ OPERATORS ON BERGMAN SPACES DEFINED ON UPPER PLANES

  • SI HO KANG;JA YOUNG KIM
    • Communications of the Korean Mathematical Society
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    • v.14 no.1
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    • pp.171-177
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    • 1999
  • We study some properties of Toeplitz operators on the Bergman spaces B\ulcorner(H\ulcorner), where H\ulcorner={x+iy : y>r}. We consider the pseudo-hyperbolic disk and the covering property. We also obtain some characterizations of compact Toeplitz operators.

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BOUNDEDNESS AND COMPACTNESS OF SOME TOEPLITZ OPERATORS

  • Kang, Si Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.3
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    • pp.467-475
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    • 2013
  • We consider the problem to determine when a Toeplitz operator is bounded on weighted Bergman spaces. We introduce some set CG of symbols and we prove that Toeplitz operators induced by elements of CG are bounded and characterize when Toeplitz operators are compact and show that each element of CG is related with a Carleson measure.

HYPONORMALITY OF TOEPLITZ OPERATORS WITH POLYNOMIAL SYMBOLS

  • Kim, Jae Myung;Lee, Youho
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.1
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    • pp.65-73
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    • 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 ${\varphi}$.