Separably Injective Banach Spaces (Lecture Notes in Mathematics)

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9783319147406: Separably Injective Banach Spaces (Lecture Notes in Mathematics)

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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“The authors provide an excellent presentation of the subject, and they manage to organize an impressive amount of material in such a way that, although they use a great variety of tools from various branches to prove the results, the work remains readable and thought-provoking. The book will be an indispensible resource for graduate students and researchers.” (Antonis N. Manoussakis, Mathematical Reviews, January, 2017)

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Antonio Aviles
Verlag: Springer-Verlag Gmbh Mrz 2016 (2016)
ISBN 10: 3319147404 ISBN 13: 9783319147406
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Buchbeschreibung Springer-Verlag Gmbh Mrz 2016, 2016. Taschenbuch. Buchzustand: Neu. Neuware - 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). 217 pp. Englisch. Artikel-Nr. 9783319147406

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