On universal spaces for the class of Banach spaces whose dual balls are uniform Eberlein compacts

Details On universal spaces for the class of Banach spaces whose dual balls are uniform Eberlein compacts On universal spaces for the class of Banach spaces whose dual balls are uniform Eberlein compacts

2011-03-22

arxiv.org/abs/1103.4259v1

Mathematics

Functional Analysis

Scientific paper

For k being the first uncountable cardinal w_1 or k being the cardinality of the continuum c, we prove that it is consistent that there is no Banach space of density k in which it is possible to isomorphically embed every Banach space of the same density which has a uniformly G\^ateaux differentiable renorming or, equivalently, whose dual unit ball with the weak* topology is a subspace of a Hilbert space (a uniform Eberlein compact space). This complements a consequence of results of M. Bell and of M. Fabian, G. Godefroy, V. Zizler that assuming the continuum hypothesis, there is a universal space for all Banach spaces of density k=c=w_1 which have a uniformly G\^ateaux differentiable renorming. Our result implies, in particular, that \beta N-N may not map continuously onto a compact subset of a Hilbert space with the weak topology of density k=w_1 or k=c and that a C(K) space for some uniform Eberlein compact space K may not embed isomorphically into l_\infty/c_0.

Affiliated with

Also associated with

No associations

Rating

On universal spaces for the class of Banach spaces whose dual balls are uniform Eberlein compacts does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On universal spaces for the class of Banach spaces whose dual balls are uniform Eberlein compacts, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On universal spaces for the class of Banach spaces whose dual balls are uniform Eberlein compacts will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-48998