A Decomposition Theorem for Frames and the Weak Feichtinger Conjecture
نویسندگان
چکیده
The constants A and B are called lower and upper frame bounds for the frame. We call a frame {fi}i∈I bounded, if there exists δ > 0 such that ‖fi‖ ≥ δ for all i ∈ I (the norms of the frame elements are always uniformly bounded from above [3, Proposition 4.6]), and unit norm, if ‖fi‖ = 1 for all i ∈ I. If {fi}i∈I is a frame only for its closed linear span, we call it a frame sequence. Those sequences which satisfy the upper inequality in (1) are called Bessel sequences. A family {fi}i∈I is a Riesz basis for H if the sequence is complete and there exist 0 < A ≤ B < ∞ such that for all sequences of scalars c = {ci}i∈I ,
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