Complementably Universal Banach Spaces, Ii

A New Class of Banach Sequence Spaces

Ja n 19 92 Isomorphism of certain weak L p spaces Denny

The Lorentz spaces play an important role in interpolation theory. They also form a class of Banach spaces generalizing the classical L spaces. In this paper, we continue the comparison of the Banach space structures of various weak L spaces begun in [2] and [3]. In [2], mimicking the construction of the Rademacher functions, it was shown that l can be embedded complementably into l. In [3], we...

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.

The Banach Space S Is Complementably Minimal and Subsequentially Prime

We first include a result of the second author showing that the Banach space S is complementably minimal. We then show that every block sequence of the unit vector basis of S has a subsequence which spans a space isomorphic to its square. By the Pe lczyński decomposition method it follows that every basic sequence in S which spans a space complemented in S has a subsequence which spans a space ...

Banach Spaces of Bounded Szlenk Index Ii

For every α < ω1 we establish the existence of a separable Banach space whose Szlenk index is ω and which is universal for all separable Banach spaces whose Szlenkindex does not exceed ω. In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with upper estimates.