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Types on stable Banach spaces

José Iovino (1998)

Fundamenta Mathematicae

 We prove a geometric characterization of Banach space stability. We show that a Banach space X is stable if and only if the following condition holds. Whenever X ^ is an ultrapower of X and B is a ball in X ^ , the intersection B ∩ X can be uniformly approximated by finite unions and intersections of balls in X; furthermore, the radius of these balls can be taken arbitrarily close to the radius of B, and the norm of their centers arbitrarily close to the norm of the center of B.  The preceding condition...

Ultrapowers of Köthe function spaces.

Yves Raynaud (1997)

Collectanea Mathematica

The ultrapowers, relative to a fixed ultrafilter, of all the Köthe function spaces with non trivial concavity over the same measure space can be represented as Köthe function spaces over the same (enlarged) measure space. The existence of a uniform homeomorphism between the unit spheres of two such Köthe function spaces is reproved.

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