Generalized Cauchy Product and Related Operators on l^p(β)

Abstract

In this paper first we give some necessary and sufficient conditions for the boundedness of the multiplication operator Df = M~,f with respect to the generalized Cauchy product ~, on `p(β). Also, under certain conditions, we give the characterization of the extended eigenvalues and extended eigenvectors of the multiplication operator M~,z on `p(β). Finally we describe the commutants of M~,z and consequently the collection of all hyperinvariant subspaces of M~,z.