Decompositions of frames and a new frame identity
نویسندگان
چکیده
If B < ∞ we call F = {fi}i∈I a Bessel sequence with Bessel bound B. If 0 < A ≤ B < ∞, then {fi}i∈I is a frame for K. If K 6= H we call {fi}i∈I a frame sequence in H. The largest A and the smallest B satisfying the above inequalities are called the optimal lower and upper frame bound and will be denoted A(F) and B(F) respectively. If A = B = λ we call this a λ-tight frame and if λ = 1 it is called a Parseval frame. If all the frame elements have the same norm we call this an equal-norm frame and if the frame elements have norm 1 it is called a unit-norm frame. If {fi}i∈I is a Bessel sequence, the synthesis operator for {fi}i∈I is the bounded linear operator T : l2(I) → H given by T (ei) = fi for all i ∈ I where {ei}i∈I is the unit vector basis of l2(I). The analysis operator for {fi}i∈I is T ∗ and satisfies:
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