Normalized weakly null sequence with no unconditional subsequence

DOI10.4064/sm-61-1-77-98zbMath0357.46025OpenAlexW1480269273MaRDI QIDQ4129941

Haskell P. Rosenthal, Bernard Maurey

Publication date: 1977

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/218176

Mathematics Subject Classification ID

Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Rings and algebras of continuous, differentiable or analytic functions (46E25)

Related Items

On the boundedness of threshold operators in \(L_1[0,1\) with respect to the Haar basis] ⋮ On asymptotic models in Banach spaces ⋮ On the solution of the scalar-plus-compact problem by Argyros and Haydon ⋮ The distortion problem ⋮ Unnamed Item ⋮ Genericity and amalgamation of classes of Banach spaces ⋮ Unnamed Item ⋮ Positional graphs and conditional structure of weakly null sequences ⋮ Unnamed Item ⋮ Separable spaces of continuous functions as Calkin algebras ⋮ Unconditional basic sequences in spaces of large density ⋮ Unconditional structures of weakly null sequences ⋮ Weakly null sequences with an unconditional subsequence ⋮ An extension of Schreier unconditionality ⋮ Joint spreading models and uniform approximation of bounded operators ⋮ A non-separable uniformly convex Banach space on which there are few operators ⋮ Embedding uniformly convex spaces into spaces with very few operators ⋮ The Unconditional Basic Sequence Problem ⋮ Some combinatorial principles for trees and applications to tree families in Banach spaces ⋮ A hereditarily indecomposable \(\mathcal L_{\infty}\)-space that solves the scalar-plus-compact problem ⋮ Elton near unconditionality of arrays ⋮ Banach spaces and Ramsey theory: some open problems ⋮ On the hereditary proximity to \(\ell _{1}\) ⋮ A class of Banach spaces with few non-strictly singular operators ⋮ Non-asymptotic $\ell_1$ spaces with unique $\ell_1$ asymptotic model ⋮ A Banach space block finitely universal for monotone bases ⋮ Interpolating hereditarily indecomposable Banach spaces ⋮ Homogeneous families on trees and subsymmetric basic sequences ⋮ Some recent discoveries in the isomorphic theory of Banach spaces ⋮ Almost isometric constants for partial unconditionality ⋮ The distortion of Hilbert space ⋮ Pre-compact families of finite sets of integers and weakly null sequences in Banach spaces ⋮ Bases of random unconditional convergence in Banach spaces ⋮ The Banach spaces of Maurey and Rosenthal and totally incomparable bases ⋮ Convex unconditionality and summability of weakly null sequences ⋮ An extremely non-homogeneous weak Hilbert space ⋮ Weakly null sequences in 𝐿₁ ⋮ On the unconditional subsequence property ⋮ Banach-Saks exponent of certain Banach spaces of sequences ⋮ The space is primary for 1 < p < ∞