• Title, Summary, Keyword: Toeplitz operators

Search Result 62, Processing Time 0.03 seconds

HYPONORMALITY OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

  • Lee, Jongrak
    • Korean Journal of Mathematics
    • /
    • v.15 no.2
    • /
    • pp.185-193
    • /
    • 2007
  • In this paper we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Bergman space $L^2_a({\mathbb{D})$ with symbol in the case of function $f+{\overline{g}}$ with polynomials $f$ and $g$. We present some necessary conditions for the hyponormality of $T_{\varphi}$ under certain assumptions about the coefficients of ${\varphi}$.

  • PDF

MATRICES OF TOEPLITZ OPERATORS ON HARDY SPACES OVER BOUNDED DOMAINS

  • Chung, Young-Bok
    • Bulletin of the Korean Mathematical Society
    • /
    • v.54 no.4
    • /
    • pp.1421-1441
    • /
    • 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 OPERATORS ON WEIGHTED ANALYTIC BERGMAN SPACES OF THE HALF-PLANE

  • Kang, Si-Ho;Kim, Ja-Young
    • Bulletin of the Korean Mathematical Society
    • /
    • v.37 no.3
    • /
    • pp.437-450
    • /
    • 2000
  • On the setting of the half-plane H={x+iy$\mid$y>0} of the complex plane, we study some properties of weighted Bergman spaces and their duality. We also obtain some characterizations of compact Toeplitz operators.

  • PDF

ESSENTIAL SPECTRA OF TOEPLITZ OPERATORS

  • Wong, M.W.
    • Bulletin of the Korean Mathematical Society
    • /
    • v.36 no.2
    • /
    • pp.357-361
    • /
    • 1999
  • The essential spectra for a class of Toeplitz operators on p, 1$\leq$p$\leq$$\infty$, are computed.

  • PDF

COMMUTATIVITY AND HYPONORMALITY OF TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACE

  • Lu, Yufeng;Liu, Chaomei
    • Journal of the Korean Mathematical Society
    • /
    • v.46 no.3
    • /
    • pp.621-642
    • /
    • 2009
  • In this paper we give necessary and sufficient conditions that two Toeplitz operators with monomial symbols acting on the weighted Bergman space commute. We also present necessary and sufficient conditions for the hyponormality of Toeplitz operators with some special symbols on the weighted Bergman space. All the results are stated in terms of the Mellin transform of the symbol.