TY  - BOOK
AU  - Aviles,Antonio
AU  - Sanchez,Felix Cabello
AU  - Castillo,Jesus M.F.
AU  - Gonzalez,Manuel
AU  - Moreno,Yolanda
TI  - Separably injective Banach spaces
T2  - Lecture notes in mathematics
SN  - 9783319147406 
U1  - 515.732 23
PY  - 2016///
CY  - Switzerland : 
PB  - Springer
KW  - Banach spaces.
KW  - Operator theory.
N1  - Includes bibliographical references and index; 1. A primer on injective Banach spaces.- 
2. Separably injective Banach spaces.- 
3. Spaces of universal disposition.- 
4. Ultraproducts of type L .- 
5. %-injectivity.- 
6. Open Problems.-
Appendix
N2  - 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
ER  -