Browsing by Subject "Toeplitz operator"

Filter results by typing the first few letters
Now showing 1 - 1 of 1
  • Thumbnail Image
    ItemOpen Access
    Toeplitz operators on arveson and dirichlet spaces
    (Birkhaeuser Science, 2007) Alpay, D.; Kaptanoǧlu, H. T.
    We define Toeplitz operators on all Dirichlet spaces on the unit ball of CN and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate some connections between Toeplitz and shift operators. © Birkhäuser Verlag Basel/Switzerland 2007.