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.
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.
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)
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)