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In Proc. Amer. Math. Soc (2005), pp. 1025-1033 Key: citeulike:11476518
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Abstract. We show that the conjectured generalization of the Bourgain-Tzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written as a finite union of Riesz basic sequences. We prove that any bounded frame can at least be written as a finite union of linear independent sequences. We further show that the two conjectures are implied by the paving conjecture. Finally, we show that Weyl-Heisenberg frames over rational lattices are finite unions of Riesz basic sequences. 1.
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