Smooth Analysis in Banach Spaces De Gruyter Series in Nonlinear Analysis and Applications 19 Smooth Analysis in Banach Spaces De Gruyter Series in Nonlinear Analysis and Applications 19 Petr Hajek October 15, 2013 Pages: Book Description: In this groundbreaking book, [Insert Author's Name] delves into the fascinating world of smooth analysis in Banach spaces, offering a comprehensive exploration of the subject matter that has never been tackled before in such depth. The author presents a detailed description of the plot, weaving together various angles of view on polynomials in both finite and infinite settings, providing a thorough and systematic approach to the more recent results and their work. The book revolves around two main themes: what is the best smoothness of a given Banach space and its structural consequences, and how large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology? The Stone-Weierstrass theorem is generalized into infinite dimensions, where measure and compactness are not available, making this book an essential reference for anyone interested in the field. Plot Summary: The story begins with an introduction to the subject of higher smoothness in separable real Banach spaces, laying the foundation for the rest of the narrative. The author then embarks on a journey to explore the more recent results and their work, presenting a detailed and systematic view of the subject. The first theme of the book focuses on what is the best smoothness of a given Banach space and its structural consequences, while the second theme delves into how large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology.

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