Frames via Unilateral Iterations of a Bounded Operator

Motivated by recent work in Dynamical Sampling, we prove a necessary and sufficient condition for a frame in a separable and infinite-dimensional Hilbert space to admit the form $\{T^n\phi {\}}_{n\ge 0}$ with $T \in B(H)$\mathrm{.}Also,acharacterizationofallthevectors$\varphi$forwhich${T^{n} \varphi }_{n \geq 0}$isaframeforsome$T \in B(H)$ is provided. Some auxiliary results on operator representations of Riesz frames are given as well.