Separably injective Banach spaces / Antonio Avilés, Félix Cabello Sánchez, Jesús M.F. Castillo...[et al.]

Auteur: Avilés, Antonio - AuteurCo-auteur: Cabello Sánchez, Félix - Auteur ; Castillo, Jesús M. F. - AuteurType de document: MonographieCollection: Lecture notes in mathematics ; 2132Langue: anglaisPays: SwisseÉditeur: Cham : Springer, 2016Description: 1 vol. (XXII-217 p.) ; 24 cm ISBN: 9783319147406 ; br. ISSN: 0075-8434Résumé: The extension problem is a main topic in many branches of mathematics, and in abstract form can be stated as follows: whether an object that has been defined in a space can be extended to any superspace and maintain its properties. One of its forms in Banach space theory is whether a bounded linear operator defined on a subspace of a Banach space can be extended to the whole space with the norm of the extension being dominated by the norm of the initial operator. The extension problem goes back to S. Banach. ... The authors provide an excellent presentation of the subject, and they manage to organize an impressive amount of material in such a way that, although they use a great variety of tools from various branches to prove the results, the work remains readable and thought-provoking. The book will be an indispensable resource for graduate students and researchers. (MSN).Bibliographie: Bibliogr. p. 205-213. Index. Sujets MSC: 46-02 Functional analysis -- Research exposition (monographs, survey articles)
46B26 Functional analysis -- Normed linear spaces and Banach spaces; Banach lattices -- Nonseparable Banach spaces
46B04 Functional analysis -- Normed linear spaces and Banach spaces; Banach lattices -- Isometric theory of Banach spaces
46A22 Functional analysis -- Topological linear spaces and related structures -- Theorems of Hahn-Banach type; extension and lifting of functionals and operators
46B08 Functional analysis -- Normed linear spaces and Banach spaces; Banach lattices -- Ultraproduct techniques in Banach space theory
En-ligne: Zentralblatt | MSN
Location Call Number Status Date Due
Salle R 12460-01 / 46 AVI (Browse Shelf) Available

Bibliogr. p. 205-213. Index

The extension problem is a main topic in many branches of mathematics, and in abstract form can be stated as follows: whether an object that has been defined in a space can be extended to any superspace and maintain its properties. One of its forms in Banach space theory is whether a bounded linear operator defined on a subspace of a Banach space can be extended to the whole space with the norm of the extension being dominated by the norm of the initial operator. The extension problem goes back to S. Banach. ... The authors provide an excellent presentation of the subject, and they manage to organize an impressive amount of material in such a way that, although they use a great variety of tools from various branches to prove the results, the work remains readable and thought-provoking.
The book will be an indispensable resource for graduate students and researchers. (MSN)

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