P. G. Dept. of Mathematics, Utkal University, Vanivihar, Bhubaneswar, 751 004, Orissa
,IN
Keywords:
Berezin Transform, Bounded Linear Operators, Bergman Space.
Abstract
Let D = {z ∈ C : |z| < 1} and σ be the map from £(L2a(D)) into L∞(D) defined as σ(T)(z) = {Tkz, kz}, where {kz}z∈D are the normalized reproducing kernels for the Bergman space L2a(D) into itself. The function σ(T) is called the Berezin transform of T. In this paper we have shown that Range(σ) is not a closed subspace of L∞(D) and give a characterization of functions in L∞(D) that are in Range(σ).