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＜電子ブック＞
Separably Injective Banach Spaces / by Antonio Avilés, Félix Cabello Sánchez, Jesús M.F. Castillo, Manuel González, Yolanda Moreno
(Lecture Notes in Mathematics. ISSN:16179692 ; 2132)

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
大きさ	XXII, 217 p : online resource
著者標目	*Avilés, Antonio author Cabello Sánchez, Félix author Castillo, Jesús M.F author González, Manuel author Moreno, Yolanda author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Operator theory FREE:Functional Analysis FREE:Operator Theory
一般注記	A primer on injective Banach spaces -- Separably injective Banach spaces -- Spaces of universal disposition -- Ultraproducts of type L∞ -- ℵ-injectivity -- Other weaker forms of injectivity -- Open Problems 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 HTTP:URL=https://doi.org/10.1007/978-3-319-14741-3

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