Compact operators on the weighted Bergman space A1([psi])
We show that a bounded linear operatorS on the weighted Bergman space A 1 ( ) is compact and the predual space A0(') of A 1 ( ) is invariant under Sif and only if Skz ! 0 as z ! @D, where kz is the normalized reproducing kernel of A 1 ( ). As an application, we give conditions for an operator in the Toeplitz algebra to be compact.