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Lecture Notes in Mathematics

Separably Injective Banach Spaces

Authors: Avilés, A., Cabello Sánchez, F., Castillo, J.M.F., González, M., Moreno, Y.

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  • This is the first book dedicated to the subject
  • Most of the material has never appeared in book form before (and all references to external results have been restricted to material which can be found in books)
  • The exposition is lively and detailed, in contrast to the typical style of mathematical papers
  • The monograph contains many annotated open problems, alternative routes and suggestions for new lines of research.
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eBook $44.99
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  • ISBN 978-3-319-14741-3
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Softcover $59.99
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  • ISBN 978-3-319-14740-6
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About this book

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.

Reviews

“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)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $44.99
price for Mexico (gross)
  • ISBN 978-3-319-14741-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for Mexico
  • ISBN 978-3-319-14740-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Separably Injective Banach Spaces
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2132
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-14741-3
DOI
10.1007/978-3-319-14741-3
Softcover ISBN
978-3-319-14740-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XXII, 217
Topics