A model for (n,p)(n,p)-hypercontractions on Banach space

In this paper we extend a model of Agler for nn-hypercontractions on Hilbert space to Banach space. This work also generalizes models of Nagy–Foias, Rovnyak–de Branges for contractions on Hilbert space to Banach space. A version of the similarity model of Rota on Banach space is also given.