Reordered Frames andWeavings

For two frames {φi }i∈I and {ψi }i∈I, the family {φi }i∈σ^∪{ψi }i∈σc is called a weaving, where I is a countable index set and σ ⊂ I. Two frames {φi }i∈I and {ψi }i∈I are called woven if all theirweavings are frameswith the same frame bounds. The concept of this manuscript is motivated by an important and interesting problem which is, under what conditions the frames {φi }i∈I and {φπ(i )}i∈I are woven for the separable Hilbert space H, where π is a permutation function on I. In this paper, the effect of reordering of the elements of weavings for frames is studied. In particular, full spark frames and muniform excess frames are studied. Also, an interesting characterization of reordered weavings by orthogonal projections is given. Finally, the effects of perturbations are considered.