Smooth Analysis in Banach Spaces / / Petr Hájek, Michal Johanis.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications
• VerfasserIn: Hájek, Petr,; Johanis, Michal,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2014]; ©2014
• Year of Publication: 2014
• Language: English
• Series: De Gruyter Series in Nonlinear Analysis and Applications , 19
• Physical Description: 1 online resource (497 p.)

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.

Table of Contents

Frontmatter -- Contents -- Introduction -- Chapter 1. Fundamental properties of smoothness -- Chapter 2. Basic properties of polynomials on Rn -- Chapter 3. Weak continuity of polynomials and estimates of coefficients -- Chapter 4. Asymptotic properties of polynomials -- Chapter 5. Smoothness and structure -- Chapter 6. Structural behaviour of smooth mappings -- Chapter 7. Smooth approximation -- Bibliography -- Notation -- Index