Smooth Analysis in Banach Spaces

Petr Hájek; Michal Johanis

Published by De Gruyter 2014

Smooth Analysis in Banach Spaces

Petr Hájek and Michal Johanis

Volume 19 in the series De Gruyter Series in Nonlinear Analysis and Applications

https://doi.org/10.1515/9783110258998

Overview
Contents

About this book

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.

Detailed exposition of the foundations of the subject
Connects several areas of research, namely polynomials on finite and infinite dimensional spaces, variational principles, renormings and structure of Banach spaces

Author / Editor information

Petr Hájek, Academy of Sciences of the Czech Republic, Prague, Czech Republic; Michal Johanis, Charles University, Prague, Czech Republic.

Reviews

"The authors have presented an impressive piece of work […]. However technical the material is they have provided detailed proofs and illuminating comments. To make their monograph self-contained they have also incorporated a lot of background material, often with full proofs." Zentralblatt für Mathematik

Topics

Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	v
Introduction Requires Authentication Unlicensed Licensed Download PDF	vii
Chapter 1. Fundamental properties of smoothness Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2. Basic properties of polynomials on Rⁿ Requires Authentication Unlicensed Licensed Download PDF	82
Chapter 3. Weak continuity of polynomials and estimates of coefficients Requires Authentication Unlicensed Licensed Download PDF	130
Chapter 4. Asymptotic properties of polynomials Requires Authentication Unlicensed Licensed Download PDF	184
Chapter 5. Smoothness and structure Requires Authentication Unlicensed Licensed Download PDF	239
Chapter 6. Structural behaviour of smooth mappings Requires Authentication Unlicensed Licensed Download PDF	328
Chapter 7. Smooth approximation Requires Authentication Unlicensed Licensed Download PDF	382
Bibliography Requires Authentication Unlicensed Licensed Download PDF	467
Notation Requires Authentication Unlicensed Licensed Download PDF	490
Index Requires Authentication Unlicensed Licensed Download PDF	493

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate Students, Researchers in Functional Analysis; Academic Libraries
Pages
- Front matter: 16
- Main content: 497
Keywords: Banach Space; Smoothness; Polynomial; Variational Principle; Approximation

eBook

Published: October 29, 2014
ISBN: 9783110258998

Hardcover

Published: September 15, 2014
ISBN: 9783110258981