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Separably Injective Banach Spaces (Paperback, 1st ed. 2016)
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Separably Injective Banach Spaces (Paperback, 1st ed. 2016)
Series: Lecture Notes in Mathematics, 2132
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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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