Banach Spaces of Almost Universal Complemented Disposition

On Banach spaces of universal disposition

We present: i) an example of a Banach space of universal disposition that is not separably injective; ii) an example of a Banach space of universal disposition with respect to finite dimensional polyhedral spaces with the Separable Complementation Property; iii) a new type of space of universal disposition nonisomorphic to the previous existing ones.

On quasi-complemented subspaces of banach spaces.

Complementably Universal Banach Spaces, Ii

The two main results are: A. If a Banach space X is complementably universal for all subspaces of c0 which have the bounded approximation property, then X∗ is non separable (and hence X does not embed into c0), B. There is no separable Banach space X such that every compact operator (between Banach spaces) factors through X. Theorem B solves a problem that dates from the 1970s.

Characterizations of almost transitive superreflexive Banach spaces

Almost transitive superreflexive Banach spaces have been considered in [7] (see also [4] and [6]), where it is shown that such spaces are uniformly convex and uniformly smooth. We prove that convex transitive Banach spaces are either almost transitive and superreflexive (hence uniformly smooth) or extremely rough. The extreme roughness of a Banach space X means that, for every element u in the ...

Quotients of Banach Spaces and Surjectively Universal Spaces

We characterize those classes C of separable Banach spaces for which there exists a separable Banach space Y not containing l1 and such that every space in the class C is a quotient of Y .