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Notes on spaces with a weak-development

Ge Y.

Fasciculi Mathematici

2007

Nr 38

17-24

Z. Li characterized spaces with a weak-development consisting of point-countable sfp-coveis by pseudo-sequence-covering, quotient, and π-s-image of metric spaces. In this paper, we omit "pseudo-sequence-covering" in the above result, and prove that a space has a weak-development consisting of point-countable sfp-covers iff it is a quotient, and TT-s-image of a metric space.

Generalizations of the c0-l1-l∞ theorem of Bessaga and Pełczyński

Wójtowicz M.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 4

373-382

Let X and Y be two Banach spaces such that Y has a subsymmetric Schauder basis (yn). We study the consequences of the following assumption: X* has a subspace isomorphic to Y. If the basis is shrinking, then X* contains a copy of Y** (Proposition 1), and if X has the so-called controlled separable projection property (in particular, if X is weakly compactly determined), then X* contains a copy of [yn*]* (Theorem 1). These results are applied for Orlicz sequence spaces.