• Title, Summary, Keyword: Toeplitz operators

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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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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 ${\varphi}$.

SPECIAL ORTHONORMAL BASIS FOR L2 FUNCTIONS ON THE UNIT CIRCLE

  • Chung, Young-Bok
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.6
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    • pp.2013-2027
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    • 2017
  • We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

NOTE ON COMMUTING TOEPLITZ OPERATORS ON THE PLURIHARMONIC BERGMAN SPACE

  • Choe, Boo-Rim;Nam, Kye-Sook
    • Journal of the Korean Mathematical Society
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    • v.43 no.2
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    • pp.259-269
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    • 2006
  • We obtain a characterization of commuting Toeplitz operators with holomorphic symbols acting on the pluriharmonic Bergman space of the polydisk. We also obtain a characterization of normal Toeplitz operators with pluriharmonic symbols. In addition, some results for special types of semi-commutators are included.

COMMUTANTS OF TOEPLITZ OPERATORS WITH POLYNOMIAL SYMBOLS ON THE DIRICHLET SPACE

  • Chen, Yong;Lee, Young Joo
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.533-542
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    • 2019
  • We study commutants of Toeplitz operators acting on the Dirichlet space of the unit disk and prove that an operator in the Toeplitz algebra commuting with a Toeplitz operator with a nonconstant polynomial symbol must be a Toeplitz operator with an analytic symbol.

ON MULTI SUBSPACE-HYPERCYCLIC OPERATORS

  • Moosapoor, Mansooreh
    • Communications of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.1185-1192
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    • 2020
  • In this paper, we introduce and investigate multi subspace-hypercyclic operators and prove that multi-hypercyclic operators are multi subspace-hypercyclic. We show that if T is M-hypercyclic or multi M-hypercyclic, then Tn is multi M-hypercyclic for any natural number n and by using this result, make some examples of multi subspace-hypercyclic operators. We prove that multi M-hypercyclic operators have somewhere dense orbits in M. We show that analytic Toeplitz operators can not be multi subspace-hypercyclic. Also, we state a sufficient condition for coanalytic Toeplitz operators to be multi subspace-hypercyclic.

NORM AND ESSENTIAL NORM ESTIMATES OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

  • Choe, Boo-Rim;Lee, Young-Joo
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.937-958
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    • 1996
  • On the setting of product of balls we consider Toeplitz operators, with symbols satisfying a certain condition, on the Bergman space. Norms and essential norms of such operators are estimated by means of certain integral quantities.

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