A normalized weakly null sequence with no shrinking subsequence in a Banach space not containing
Stability in Banach spaces.
Ordinal indices in Banach spaces.
The Distortion of Hilbert Space.
The unit ball of every infinite-dimensional normed linear space contains a (1+ɛ)-separated sequence
Subspaces of which embed into
On the structure of separable spaces (1 < p < ∞)
Banach spaces of bounded Szlenk index
For a countable ordinal α we denote by the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each admits a separable, reflexive universal space. We also show that spaces in the class embed into spaces of the same class with a basis. As a consequence we deduce that each is analytic in the Effros-Borel structure of subspaces of C[0,1].
On asymptotically symmetric Banach spaces
A Banach space X is asymptotically symmetric (a.s.) if for some C < ∞, for all m ∈ ℕ, for all bounded sequences , 1 ≤ i ≤ m, for all permutations σ of 1,...,m and all ultrafilters ₁,...,ₘ on ℕ, . We investigate a.s. Banach spaces and several natural variations. X is weakly a.s. (w.a.s.) if the defining condition holds when restricted to weakly convergent sequences . Moreover, X is w.n.a.s. if we restrict the condition further to normalized weakly null sequences. If X is a.s. then all spreading...
Banach spaces of bounded Szlenk index II
For every α < ω₁ we establish the existence of a separable Banach space whose Szlenk index is and which is universal for all separable Banach spaces whose Szlenk index does not exceed . In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with Tsirelson type upper estimates.
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