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< …

EXAMPLES OF ASYMPTOTIC l1 BANACH SPACES Introduction A Banach space (X, ·) is λ-distortable
(λ > 1) if there exists an eq Page 1 TRANSACTIONS OF THE AMERICAN MATHEMATICAL …

The following dichotomy is proved. Every Banach space either contains a subspace
isomorphic to $\ell^ 1$, or it has an infinite-dimensional closed subspace which is a quotient …

For a Banach space $ X $ denote by $\mathcal {L}(X) $ the algebra of bounded linear
operators on $ X $, by $\mathcal {K}(X) $ the compact operator ideal on $ X $, and by $ Cal …

We study the interplay between Banach space theory and theory of analytic P-ideals.
Applying the observation that, up to isomorphism, all Banach spaces with unconditional …

A separable Banach space X satisfies the invariant subspace property (ISP) if every
bounded linear operator T∈ ℒ (X) admits a non-trivial closed invariant subspace. In this …

A well known argument of James yields that if a Banach space X contains ℓ 1 n's uniformly,
then X contains ℓ 1 n's almost isometrically. In the first half of the paper we extend this idea …

For each $ n\in\mathbb {N} $ a Banach space $\mathfrak {X} _ {_ {^{0, 1}}}^{n} $ is
constructed having the property that every normalized weakly null sequence generates …

For every Banach space X with a Schauder basis, consider the Banach algebra RI⊕ Kdiag
(X) of all diagonal operators that are of the form λI+ K. We prove that RI⊕ Kdiag (X) is a …

We study Tsirelson type spaces of the form T [(ℳ︁k, θk) lk= 1] defined by a finite sequence
(ℳ︁k) lk= 1 of compact families of finite subsets of ℕ. Using an appropriate index, denoted …