Smooth Analysis in Banach Spaces
Oct 2014 · De Gruyter Series in Nonlinear Analysis and Applications Book 19 · Walter de Gruyter GmbH & Co KG
Ebook
513
Pages
About this ebook
This book is about the subject of higher smoothness in separable real Banach spaces. It brings together several angles of view on polynomials, both in finite and infinite setting. Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into infinite dimension where measure and compactness are not available?
The subject of infinite dimensional real higher smoothness is treated here for the first time in full detail, therefore this book may also serve as a reference book.
About the author
Petr Hájek, Academy of Sciences of the Czech Republic, Prague, Czech Republic; Michal Johanis, Charles University, Prague, Czech Republic.
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