Selecting basic sequences in φ-stable Banach spaces

Tadeusz Figiel, et al. "Selecting basic sequences in φ-stable Banach spaces." Studia Mathematica 159.3 (2003): 499-515. <http://eudml.org/doc/285351>.

@article{TadeuszFigiel2003,
abstract = { In this paper we make use of a new concept of φ-stability for Banach spaces, where φ is a function. If a Banach space X and the function φ satisfy some natural conditions, then X is saturated with subspaces that are φ-stable (cf. Lemma 2.1 and Corollary 7.8). In a φ-stable Banach space one can easily construct basic sequences which have a property P(φ) defined in terms of φ (cf. Theorem 4.5). This leads us, for appropriate functions φ, to new results on the existence of unconditional basic sequences with some special properties as well as new proofs of some known results. In particular, we get a new proof of the Gowers dichotomy theorem which produces the best unconditionality constant (also in the complex case). },
author = {Tadeusz Figiel, Ryszard Frankiewicz, Ryszard A. Komorowski, Czesław Ryll-Nardzewski},
journal = {Studia Mathematica},
keywords = {unconditional basic sequence; Gowers' dichotomy theorem},
language = {eng},
number = {3},
pages = {499-515},
title = {Selecting basic sequences in φ-stable Banach spaces},
url = {http://eudml.org/doc/285351},
volume = {159},
year = {2003},
}

TY - JOUR
AU - Tadeusz Figiel
AU - Ryszard Frankiewicz
AU - Ryszard A. Komorowski
AU - Czesław Ryll-Nardzewski
TI - Selecting basic sequences in φ-stable Banach spaces
JO - Studia Mathematica
PY - 2003
VL - 159
IS - 3
SP - 499
EP - 515
AB - In this paper we make use of a new concept of φ-stability for Banach spaces, where φ is a function. If a Banach space X and the function φ satisfy some natural conditions, then X is saturated with subspaces that are φ-stable (cf. Lemma 2.1 and Corollary 7.8). In a φ-stable Banach space one can easily construct basic sequences which have a property P(φ) defined in terms of φ (cf. Theorem 4.5). This leads us, for appropriate functions φ, to new results on the existence of unconditional basic sequences with some special properties as well as new proofs of some known results. In particular, we get a new proof of the Gowers dichotomy theorem which produces the best unconditionality constant (also in the complex case).
LA - eng
KW - unconditional basic sequence; Gowers' dichotomy theorem
UR - http://eudml.org/doc/285351
ER -