Smooth Analysis in Banach Spaces

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...

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Bibliographic Details
Main Authors: Hájek, Petr, Johanis, Michal
Format: eBook Book
Language:English
Published: Germany De Gruyter 2014
De Gruyter, Inc
Edition:1
Series:De Gruyter Series in Nonlinear Analysis and Applications
Subjects:
Approximation
Banach Space
Banach spaces
MATHEMATICS
MATHEMATICS / Functional Analysis
MATHEMATICS / Mathematical Analysis
MATHEMATICS / Reference
Mathematics. Analysis
Normed linear spaces
Polynomial
Polynomials
Smoothness
Variational Principle
Polynomial
Banach Space
Approximation
Variational Principle
Smoothness
ISBN:3110258994, 9783110258998, 9783110258981, 3110258986, 9783110391992, 3110391996
Online Access:Get full text
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Summary: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.
Bibliography:Includes bibliographical references (p. [467]-489) and index
ISBN:3110258994
9783110258998
9783110258981
3110258986
9783110391992
3110391996
DOI:10.1515/9783110258998