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Abstrakty
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).
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).
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
499-515
Opis fizyczny
Daty
wydano
2003
Twórcy
autor
- Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
autor
- Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
autor
- Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
autor
- Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-3-10