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Separably injective Banach spaces

Aviles, Antonio.

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Separably injective Banach spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Separably injective Banach spaces/ by Antonio Aviles ... [et al.].
other author:	Aviles, Antonio.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	xxii, 217 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Banach spaces. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-14741-3
ISBN:	9783319147413

Separably injective Banach spaces
Separably injective Banach spaces[electronic resource] /by Antonio Aviles ... [et al.]. - Cham :Springer International Publishing :2016. - xxii, 217 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21320075-8434 ;. - Lecture notes in mathematics ;2046..

This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines of research.

ISBN: 9783319147413

Standard No.: 10.1007/978-3-319-14741-3doiSubjects--Topical Terms:

579190
Banach spaces.

LC Class. No.: QA322.2

Dewey Class. No.: 515.732

Separably injective Banach spaces
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245 0 0 $a Separably injective Banach spaces $h [electronic resource] / $c by Antonio Aviles ... [et al.].
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a xxii, 217 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2132
520 $a This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines of research.
650 0 $a Banach spaces. $3 579190
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Operator Theory. $3 897311
700 1 $a Aviles, Antonio. $3 2186948
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Lecture notes in mathematics ; $v 2046. $3 1534285
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-14741-3
950 $a Mathematics and Statistics (Springer-11649)