Separably Injective Banach Spaces

Nonfiction, Science & Nature, Mathematics, Functional Analysis
Cover of the book Separably Injective Banach Spaces by Antonio Avilés, Yolanda  Moreno, Manuel González, Jesús M.F. Castillo, Félix Cabello Sánchez, Springer International Publishing
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Author: Antonio Avilés, Yolanda Moreno, Manuel González, Jesús M.F. Castillo, Félix Cabello Sánchez ISBN: 9783319147413
Publisher: Springer International Publishing Publication: March 26, 2016
Imprint: Springer Language: English
Author: Antonio Avilés, Yolanda Moreno, Manuel González, Jesús M.F. Castillo, Félix Cabello Sánchez
ISBN: 9783319147413
Publisher: Springer International Publishing
Publication: March 26, 2016
Imprint: Springer
Language: English

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.

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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.

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