P-Frames generated by operator actions in Banach spaces

Abstract Motivated by recent research in dynamical sampling and frame properties of systems from iterative actions of operators in Hilbert spaces, we give generalizations of such a Hilbert frame to a large class of frames in Banach spaces, the so-called p-frames. Let X be an infinite-dimensional separable Banach space with dual space X∗. The main purpose of this paper is to investigate the p-frames having the form {Tnφ}∞n=0 for some linear operator T : X∗ → X∗ and φ ∈ X∗. Similar to the frames in Hilbert spaces, we give various characterizations of the p-frames having such representation for a bounded operator T. In particular, we prove that any q-Riesz basis for X∗ has the form {Tnφ}∞n=0 for some injective bounded operator T : X∗ → X∗ with closed range.