Characterizations of woven frames

Abstract: In a separable Hilbert space $\mathcal H$, two frames ${f_i}{i \in I}$ and ${g_i}{i \in I}$ are said to be woven if there are constants $0<A \leq B$ so that for every $\sigma \subset I$, ${f_i}{i \in \sigma} \cup {g_i}{i \in \sigma ^c}$ forms a frame for $\mathcal H$ with the universal bounds $A, B$. This article provides methods of constructing woven frames. In particular, bounded linear operators are used to create woven frames from a given frame. Several examples are discussed to validate the results. Moreover, the notion of woven frame sequences is introduced and characterized.