Composition operators on Banach spaces of formal power series
Let be a sequence of positive numbers and . We consider the space of all power series such that . Suppose that and for some nonnegative integer . We show that if is compact on , then the non-tangential limit of has modulus greater than one at each boundary point of the open unit disc. Also we show that if is Fredholm on , then must be an automorphism of the open unit disc.