• Title, Summary, Keyword: Toeplitz operator

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SLANT H-TOEPLITZ OPERATORS ON THE HARDY SPACE

  • Gupta, Anuradha;Singh, Shivam Kumar
    • Journal of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.703-721
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    • 2019
  • The notion of slant H-Toeplitz operator $V_{\phi}$ on the Hardy space $H^2$ is introduced and its characterizations are obtained. It has been shown that an operator on the space $H^2$ is a slant H-Toeplitz if and only if its matrix is a slant H-Toeplitz matrix. In addition, the conditions under which slant Toeplitz and slant Hankel operators become slant H-Toeplitz operators are also obtained.

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.

MATRICES OF TOEPLITZ OPERATORS ON HARDY SPACES OVER BOUNDED DOMAINS

  • Chung, Young-Bok
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.4
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    • pp.1421-1441
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    • 2017
  • We compute explicitly the matrix represented by the Toeplitz operator on the Hardy space over a smoothly finitely connected bounded domain in the plane with respect to special orthonormal bases consisting of the classical kernel functions for the space of square integrable functions and for the Hardy space. The Fourier coefficients of the symbol of the Toeplitz operator are obtained from zeroth row vectors and zeroth column vectors of the matrix. And we also find some condition for the product of two Toeplitz operators to be a Toeplitz operator in terms of matrices.

TOEPLITZ TYPE OPERATOR IN ℂn

  • Choi, Ki Seong
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.4
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    • pp.697-705
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    • 2014
  • For a complex measure ${\mu}$ on B and $f{\in}L^2_a(B)$, the Toeplitz operator $T_{\mu}$ on $L^2_a(B,dv)$ with symbol ${\mu}$ is formally defined by $T_{\mu}(f)(w)=\int_{B}f(w)\bar{K(z,w)}d{\mu}(w)$. We will investigate properties of the Toeplitz operator $T_{\mu}$ with symbol ${\mu}$. We define the Toeplitz type operator $T^r_{\psi}$ with symbol ${\psi}$, $$T^r_{\psi}f(z)=c_r\int_{B}\frac{(1-{\parallel}w{\parallel}^2)^r}{(1-{\langle}z,w{\rangle})^{n+r+1}}{\psi}(w)f(w)d{\nu}(w)$$. We will also investigate properties of the Toeplitz type operator with symbol ${\psi}$.

COMPUTATION OF THE MATRIX OF THE TOEPLITZ OPERATOR ON THE HARDY SPACE

  • Chung, Young-Bok
    • Communications of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1135-1143
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    • 2019
  • The matrix representation of the Toeplitz operator on the Hardy space with respect to a generalized orthonormal basis for the space of square integrable functions associated to a bounded simply connected region in the complex plane is completely computed in terms of only the Szegő kernel and the Garabedian kernels.

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 ${\tilde{\nu}}$.