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AbstractLet B be a separable Banach space and let X=B* be separable. We prove that if B has finite Szlenk index (for all ε > 0) then B can be renormed to have the weak* uniform Kadec-Klee property.… (More)

The Gaussian correlation conjecture states that for any two symmetric, convex sets in n-dimensional space and for any centered, Gaussian measure on that space, the measure of the intersection is… (More)

The unit sphere of Hilbert space, ℓ2, is shown to contain a remarkable sequence of nearly orthogonal sets. Precisely, there exist a sequence of sets of norm one elements of ℓ2, (Ci)i=1∞, and reals… (More)

AbstractLet S⊂ℝd be a bounded subset with positive Lebesgue measure. The Paley-Wiener space associated to S, PWS, is defined to be the set of all square-integrable functions on ℝd whose Fourier… (More)

This paper deals with the following types of problems: Assume a Banach space $X$ has some property (P). Can it be embedded into some Banach space $Z$ with a finite dimensional decomposition having… (More)

We study some questions concerning the structure of the set of spreading models of a separable infinite-dimensional Banach space $X$. In particular we give an example of a reflexive $X$ so that all… (More)

We give examples of two Banach spaces. One Banach space has no spreading model which contains l p (1 ≤ p < ∞) or c o. The other space has an unconditional basis for which l p (1 ≥ p < ∞) and c o are… (More)

We prove that the Banach space $(\bigoplus_{n=1}^{\infty}\ell_{p}^{n})_{\ell_{q}}$, which is isomorphic to certain Besov spaces, has a greedy basis whenever 1≤p≤∞ and 1<q<∞. Furthermore, the Banach… (More)

We consider the X-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial… (More)

It is well known that the only proper non-trivial norm-closed ideal in the algebra L(X) for X = ℓ p (1 p < ∞) or X = c 0 is the ideal of compact operators. The next natural question is to describe… (More)