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We give a new explicit construction of n×N matrices satisfying the Restricted Isometry Property (RIP). Namely, for some ε > 0, large N , and any n satisfying N1−ε ≤ n ≤ N , we construct RIP matrices… (More)

We consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the Thresholding Greedy Algorithm (TGA). In particular, we continue the study of almost greedy… (More)

A moment inequality is proved for sums of independent random variables in the Lorentz spaces LPtq, thus extending an inequality of Rosenthal. The latter result is used in combination with a square… (More)

We consider some theoretical greedy algorithms for approximation in Banach spaces with respect to a general dictionary. We prove convergence of the algorithms for Banach spaces which satisfy certain… (More)

Let 1 p ∞ and let X be a Banach space with a semi-normalized strongly asymptotic p basis (ei). If X is minimal and 1 p < 2, then X is isomorphic to a subspace of p. If X is minimal and 2 p < ∞, or if… (More)

We give a new explicit construction of n x N matrices satisfying the Restricted Isometry Property (RIP). Namely, for some ε>0, large k and k<sup>2-ε</sup> ≤ N ≤ k<sup>2+ε</sup>, we construct RIP… (More)

We provide a Laakso construction to prove that the property of having an equivalent norm with the property (β) of Rolewicz is qualitatively preserved via surjective uniform quotient mappings between… (More)

A sequence {fn} of strongly-measurable functions taking values in a Banach space X is scalarly null a.e. (resp. scalarly null in measure) if x∗fn → 0 a.e. (resp. x∗fn → 0 in measure) for every x∗ ∈… (More)

Let 1 p ∞ and let X be a Banach space with a semi-normalized strongly asymptotic p basis (ei). If X is minimal and 1 p < 2, then X is isomorphic to a subspace of p. If X is minimal and 2 p < ∞, or if… (More)