Separably injective Banach spaces / Antonio Avilés, Félix Cabello Sánchez, Jesús M.F. Castillo, Manuel González, Yolanda Moreno.

Format:

Book

Author/Creator:

Avilés, Antonio, author.

Cabello Sánchez, Félix, author.

Castillo, Jesús M. F., author.

González, Manuel, 1957- author.

Moreno Koch, Yolanda, author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2132.

Lecture notes in mathematics, 0075-8434 ; 2132

Language:

English

Subjects (All):

Banach spaces.

Operator theory.

Physical Description:

xxii, 217 pages ; 24 cm.

Place of Publication:

Switzerland : Springer, [2016]

Summary:

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 l8/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L8 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.

Notes:

Includes bibliographical references (pages 205-213) and index.

ISBN:

3319147404

9783319147406

OCLC:

898418590