Cyclic vectors and invariant subspaces for the backward shift operator
R. G. Douglas, H. S. Shapiro, A. L. Shields (1970)
Annales de l'institut Fourier
Similarity:
The operator of multiplication by on the Hardy space of square summable power series has been studied by many authors. In this paper we make a similar study of the adjoint operator (the “backward shift”). Let denote the cyclic subspace generated by , that is, the smallest closed subspace of that contains . If , then is called a cyclic vector for . Theorem : is a cyclic vector if and only if there is a function , meromorphic and of bounded Nevanlinna...