Weaving properties of Hilbert space frames

Abstract

We will prove some new results in the theory of Weaving Frames. Two frames {φi}iεI and {Ψ_i}iεI in a Hilbert space H are woven if there are constants 0 <; A ≤ B so that for every subset σ ⊂ I, the family {φ_i}_iεσ ∪ {ψ_i}_iεσc is a frame for H with frame bounds A, B. We begin by introducing the main results in weaving frames. We then prove some new basic properties. This is followed by showing a fundamental connection between frames and projections, providing intuition on woven frames. Finally, a weaving equivalent of an unconditional basis for weaving Riesz bases is considered.