Smooth analysis in Banach spaces (De Gruyter Series in by Petr / Johanis, Michal Hájek

By Petr / Johanis, Michal Hájek

This bookis aboutthe topic of upper smoothness in separable genuine Banach spaces.It brings jointly a number of angles of view on polynomials, either in finite and countless setting.Also a slightly thorough and systematic view of the newer effects, and the authors paintings is given. The publication revolves round major extensive questions: what's the top smoothness of a given Banach area, and its structural effects? How huge is a offer of gentle capabilities within the feel of approximating non-stop capabilities within the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into countless measurement the place degree and compactness are usually not available?The topic of endless dimensional genuine better smoothness is treatedherefor the 1st time in complete aspect, for that reason this booklet can also function a reference book.

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