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Separably Injective Banach Spaces - Antonio Avilés, Félix Cabello Sánchez, Jesús M.F. Castillo, Manuel González, Yolanda Moreno

Separably Injective Banach Spaces

Buch | Softcover
XXII, 217 Seiten
2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-14740-6 (ISBN)
CHF 74,85 inkl. MwSt

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.

A primer on injective Banach spaces.- Separably injective Banach spaces.- Spaces of universal disposition.- Ultraproducts of type L .- -injectivity.- Other weaker forms of injectivity.- Open Problems.

"This book is a valuable contribution to the literature on Banach spaces." (David Yost, zbMATH 1379.46002, 2018)

"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)

Erscheint lt. Verlag 27.3.2016
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo XXII, 217 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte 46A22,46B03,46B08,46M10,46M18,26B26,54B30. • Extension of operators • Separably injective Banach spaces • Set theoretic axioms and cardinal restrictions • Spaces of universal disposition • Ultraproducts of script L infinity spaces
ISBN-10 3-319-14740-4 / 3319147404
ISBN-13 978-3-319-14740-6 / 9783319147406
Zustand Neuware
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