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This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods. It will be of interest to researchers for its methods and open problems, and to students for the exposition of techniques and examples.

Functional analysis --- Banach spaces. --- Ultraproducts. --- Duality theory (Mathematics) --- Banach spaces --- Ultraproducts --- Calculus --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Banach [Espaces de ] --- Banach [Ruimten van ] --- Dualiteit [Theorie van de ] (Wiskunde) --- Dualité [Théorie de la ] (Mathématiques) --- Mathematics duality theory --- Theorie van de dualiteit (Wiskunde) --- Théorie de la dualité (Mathématiques) --- Functional analysis. --- Topology. --- Geometry. --- Functional Analysis. --- Euclid's Elements --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

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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.

Calculus --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Functional analysis. --- Operator theory. --- Functional Analysis. --- Operator Theory. --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science