Smooth analysis in Banach spaces
( De Gruyter Series in Nonlinear Analysis and Applications )
Publication series ：De Gruyter Series in Nonlinear Analysis and Applications
Author： Hájek Petr; Johanis Michal
Publisher： De Gruyter
Publication year： 2014
E-ISBN: 9783110391992
P-ISBN(Paperback): 9783110258981
Subject： O177.2 Banach space and linear operator theory
Keyword： 数学
Language： ENG
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Description
This bookis aboutthe 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 treatedherefor the first time in full detail, therefore this book may also serve as a reference book.