(Ebook) Smooth Analysis in Banach Spaces by Petr Hájek, Michal Johanis ISBN 9783110258981, 9783110258998, 9783110391992, 3110258986, 3110258994, 3110391996, B0138MXDTG

(Ebook) Smooth Analysis in Banach Spaces by Petr Hájek, Michal Johanis ISBN 9783110258981, 9783110258998, 9783110391992, 3110258986, 3110258994, 3110391996, B0138MXDTG

Main subject categories: • Isomorphic theory (including renorming) of Banach spaces • Normed modules and Banach modules, topological modules • Continuous and differentiable maps in nonlinear functional analysis • Translation • Geometry and structure of normed linear spaces • Derivatives of functions in infinite-dimensional spacesThis 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.