Smooth analysis in Banach spaces /

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 ar...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Hájek, Petr
Otros Autores: Johanis, Michal
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin ; München ; Boston : DE GRUYTER, 2014.
Edición:2014.
Colección:De Gruyter series in nonlinear analysis and applications.
Temas:
Banach spaces.
Normed linear spaces.
Polynomials.
Espaces de Banach.
Espaces linéaires normés.
Polynômes.
Banach spaces
Normed linear spaces
Polynomials
Polynom
Banach-Raum
Stetige Abbildung
Glatte Funktion
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Introduction; Chapter 1. Fundamental properties of smoothness; 1. Multilinear mappings and polynomials; 2. Complexification; 3. Fréchet smoothness; 4. Taylor polynomial; 5. Smoothness classes; 6. Power series and their convergence; 7. Complex mappings; 8. Analytic mappings; 9. Notes and remarks; Chapter 2. Basic properties of polynomials on Rn; 1. Spaces of polynomials on Rn; 2. Cubature formulae; 3. Estimates related to Chebyshev polynomials; 4. Polynomials and L_p-norms on Rn; 5. Polynomial identities; 6. Estimates of coefficients of polynomials; 7. Notes and remarks.
  • Chapter 3. Weak continuity of polynomials and estimates of coefficients1. Tensor products and spaces of multilinear mappings; 2. Weak continuity and spaces of polynomials; 3. Weak continuity and _1; 4. (p, q)-summing operators; 5. Estimates of coefficients of multilinear mappings; 6. Bohr radius; 7. Notes and remarks; Chapter 4. Asymptotic properties of polynomials; 1. Finite representability and ultraproducts; 2. Spreading models; 3. Polynomials and p-estimates; 4. Separating polynomials. Symmetric and sub-symmetric polynomials; 5. Stabilisation of polynomials.
  • 6. Sub-symmetric polynomials on Rn7. Polynomial algebras on Banach spaces; 8. Notes and remarks; Chapter 5. Smoothness and structure; 1. Convex functions; 2. Smooth bumps and structure I; 3. Smooth variational principles; 4. Smooth bumps and structure II; 5. Local dependence on finitely many coordinates; 6. Isomorphically polyhedral spaces; 7. L_p spaces; 8. C(K) spaces; 9. Orlicz spaces; 10. Notes and remarks; Chapter 6. Structural behaviour of smooth mappings; 1. Weak uniform continuity and higher smoothness; 2. Bidual extensions; 3. Class ==========W.
  • 4. Uniformly smooth mappings from C(K), K scattered5. Uniformly smooth mappings from ==========W-spaces; 6. Fixing the canonical basis of c_0; 7. Ranges of smooth mappings; 8. Harmonic behaviour of smooth mappings; 9. Notes and remarks; Chapter 7. Smooth approximation; 1. Separation; 2. Approximation by polynomials; 3. Approximation by real-analytic mappings; 4. Infimal convolution; 5. Approximation of continuous mappings and partitions of unity; 6. Non-linear embeddings into c_0(); 7. Approximation of Lipschitz mappings; 8. Approximation of C1-smooth mappings; 9. Approximation of norms.
  • 10. Notes and remarksBibliography; Notation; Index.

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