TVC 68. Ordered Banach spaces [French]

By Richard Becker

pr face de Gilles Godefroy Ce livre traite des espaces de Banach B, ordonn s par un c ne convexe ferm X, qui ne sont pas n cessairement r ticul s. Le sujet s'est d velopp gr ce aux travaux de G. Krein (1940), V.L. Klee (1955) et T. Ando (1962). R cemment, de nouveaux r sultats ont t obtenus qui sont l'origine de ce livre; en particulier, on associe chaque c ne convexe X, contenu dans un espace de Banach B, un indice i(X), qui intervient dans divers tudes: titre d'exemple l'exploration de certaines propri t s des op rateurs lin aires positifs. De plus, quand X est un c ne normal alors l'indice permet de d terminer les espaces lp de dimension finie (de dimension arbitraire) immerg s dans B dont les vecteurs de base appartiennent X. Ce livre est auto-suffisant et compr hensible par des tudiants en Master math matiques ou toute personne ayant de bonnes connaissances en analyse. This book is devoted to the study of Banach spaces, ordered by a convex cone, which are not necessarily Banach lattices. Basic results were obtained in this domain by G. Krein (1940), V.L. Klee (1955) and T. Ando (1962). After that, the topic was rather dormant during 30 years. But, after this period, new results were obtained, which are the topic of this book; namely, to every convex cone X, contained in a Banach space B, we associate an index i(X), which is involved in various topics: for example to investigate when every positive linear operator from a C(K) space to B is p-summing. Moreover, when X is a normal cone (roughly speaking, when X is sharp) then this index enables us to provide finite dimensional lp spaces (of arbitrary dimension) embedded in B, whose basic vectors are contained in X. This book is self contained and is understandable by a graduate student having a good knowledge in Analysis.

• Format: Paperback
• Language: French
• ISBN: 2705667210
• ISBN13: 9782705667214
• Release Date: March 2008
• Publisher: Hermann
• Length: 154 Pages
• Weight: 0.50 lbs.
• Dimensions: 0.3" x 6.1" x 9.2"