1,822 research outputs found
Weakly Lindelof determined Banach spaces not containing
The class of countably intersected families of sets is defined. For any such
family we define a Banach space not containing \ell^{1}(\NN ). Thus we obtain
counterexamples to certain questions related to the heredity problem for W.C.G.
Banach spaces. Among them we give a subspace of a W.C.G. Banach space not
containing \ell^{1}(\NN ) and not being itself a W.C.G. space
Examples of asymptotically \ell_^1 Banach spaces
Two examples of asymptotic Banach spaces are given. The first,
, has an unconditional basis and is arbitrarily distortable. The second,
, does not contain any unconditional basic sequence. Both are spaces of the
type of Tsirelson. We thus answer a question raised by W.T.Gowers
Examples of k-iterated spreading models
It is shown that for every and every spreading sequence
that generates a uniformly convex Banach space ,
there exists a uniformly convex Banach space admitting
as a -iterated spreading model, but not as a
-iterated one.Comment: 16 pages, no figure
Complexity of weakly null sequences
We introduce an ordinal index which measures the complexity of a weakly null
sequence, and show that a construction due to J. Schreier can be iterated to
produce for each alpha < omega_1, a weakly null sequence (x^{alpha}_n)_n in
C(omega^{omega^{alpha}})) with complexity alpha. As in the Schreier example
each of these is a sequence of indicator functions which is a suppression-1
unconditional basic sequence. These sequences are used to construct
Tsirelson-like spaces of large index. We also show that this new ordinal index
is related to the Lavrentiev index of a Baire-1 function and use the index to
sharpen some results of Alspach and Odell on averaging weakly null sequences
Interpolating hereditarily indecomposable Banach spaces
It is shown that every Banach space either contains or it has an
infinite dimensional closed subspace which is a quotient of a H.I. Banach
space.Further on, , , is a quotient of a H.I Banach
space
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