Weaving properties of Hilbert space frames

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.