Pointwise multiplication operators on weighted Banach spaces of analytic functions

Abstract

For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator Mφ, Mφ(f) = φf, on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when Mφ is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map M'φ.