Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Argyros, Spiros (1950-....)
Titre(s) : Ramsey methods in analysis [Texte électronique] / Spiros A. Argyros, Stevo Todorcevic
Publication : Basel ; Boston : Birkhäuser, cop. 2005
Description matérielle : 1 online resource (257 pages)
Collection : Advanced courses in mathematics, CRM Barcelona
Note(s) : Includes bibliographical references (pages 247-252) and index
"This book introduces graduate students and researchers to the study of the geometry
of Banach spaces using combinatorial methods. The combinatorial, and in particular
the Ramsey-theoretic, approach to Banach space theory is not new; it can be traced
back as early as the 1970s. Its full appreciation, however, came only during the last
decade or so, after some of the most important problems in Banach space theory were
solved, such as, for example, the distortion problem, the unconditional basic sequence
problem, and the homogeneous space problem. The book covers most of these advances,
but one of its primary purposes is to discuss some of the recent advances that are
not present in survey articles of these areas. We show, for example, how to introduce
a conditional structure to a given Banach space under construction that allows us
to essentially prescribe the corresponding space of non-strictly singular operators.
We also apply the Nash-Williams theory of fronts and barriers in the study of Cezaro
summability and unconditionality present in basic sequences inside a given Banach
space. We further provide a detailed exposition of the block-Ramsey theory and its
recent deep adjustments relevant to the Banach space theory due to Gowers."--Jacket
Autre(s) auteur(s) : Todorčević, Stevo (1955-....). Fonction indéterminée
Sujet(s) : Espaces linéaires normés
Ramsey, Théorie de
Théorie des ensembles
Indice(s) Dewey :
515.732 (23e éd.) = Espaces de Banach
Identifiants, prix et caractéristiques : ISBN 9783764373603
Identifiant de la notice : ark:/12148/cb44714632p
Notice n° :
FRBNF44714632
(notice reprise d'un réservoir extérieur)
Table des matières : Saturated and Conditional Structures in Banach Spaces ; Tsirelson and Mixed Tsirelson
Spaces ; Tree Complete Extensions of a Ground Norm ; Hereditarily Indecomposable
Extensions with a Schauder Basis ; The Space of the Operators for Hereditarily Indecomposable
Banach Spaces ; Examples of Hereditarily Indecomposable Extensions ; The Space
