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- Fouad Chaatit
- 1996

We show that any separable stable Banach space can be represented as a group of isometries on a separable reflexive Banach space, which extends a result of S. Guerre and M. Levy. As a consequence, we can then represent homeomorphically its space of types.

- F Chaatit
- 1995

We prove that if X is an infinite dimensional Banach lattice with a weak unit then there exists a probability space (Ω, Σ, µ) so that the unit sphere S(L 1 (Ω, Σ, µ) is uniformly homeomorphic to the unit sphere S(X) if and only if X does not contain l n ∞ 's uniformly.

- F Chaatit, V Mascioni, H Rosenthal
- 2008

It is proved that every function of finite Baire index on a separable metric space K is a D-function, i.e., a difference of bounded semi-continuous functions on K. In fact it is a strong D-function, meaning it can be approximated arbitrarily closely in D-norm, by simple D-functions. It is shown that if the n th derived set of K is non-empty for all finite… (More)

We prove that a Banach lattice X which does not contain the l n ∞-uniformly has an equivalent norm which is uniformly Kadec-Klee for a natural topology τ on X. In case the Banach lattice is purely atomic, the topology τ is the coordinatewise convergence topology. Abstract We prove that a Banach lattice X which does not contain the l n ∞-uniformly has an… (More)

- F Chaatit, H Rosenthal
- 1999

Extrinsic and intrinsic characterizations are given for the class DSC(K) of differences of semi-continuous functions on a Polish space K, and also decomposition characterizations of DSC(K) and the class PS(K) of pointwise stabilizing functions on K are obtained in terms of behavior restricted to ambiguous sets. The main, extrinsic characterization is given… (More)

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