Abstract :
With each composition operator C fsf(w acting between classical Bergman w
spaces Ap and Aq, 1Fp, q-`, we associate in a natural way a sequence of
non-negative scalars j k , kgN. Our main result states that the composition
operator belongs to a prescribed quasi-Banach ideal A if and only if the diagonal
operator D : lpªlqgiven by a .¬ a j . belongs to A. Conversely, we show j k k k
that for any l )max 2rqy2rp, 0.and k gR there exists a composition operator
C : ApªAqwhose associated sequence is equivalent to.kyl log k.k, kG2. w
This provides an effective tool to separate quasi-Banach ideals by means of
composition operators. The results can be generalized to standard weighted
Bergman spaces and beyond.
