Analytic functions into Banach spaces and a new characterization for isomorphic embeddings

Abstract

Let T : E → F T:E \to F be a continuous linear injection between complex Banach spaces. It is shown that T T is a topological monomorphism if and only if every function f : D → E f:D \to E on the open unit disc of the complex plane, for which T ∘ f T \circ f is analytic, is itself analytic.