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Orthonormal systems and Banach space geometry /
Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advant...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
©1998.
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| Colección: | Encyclopedia of mathematics and its applications ;
v. 70. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half-title; Title; Copyright; Contents; Preface; Introduction; 0 Preliminaries; 0.1 Banach spaces and operators; 0.2 Finite dimensional spaces and operators; 0.3 Classical sequence spaces; 0.4 Classical function spaces; 0.5 Lorentz spaces; 0.6 Interpolation methods; 0.7 Summation operators; 0.8 Finite representability and ultrapowers; 0.9 Extreme points; 0.10 Various tools; 1 Ideal norms and operator ideals; 1.1 Ideal norms; 1.2 Operator ideals; 1.3 Classes of Banach spaces; 2 Ideal norms associated with matrices; 2.1 Matrices; 2.2 Parseval ideal norms and 2-summing operators
- 2.3 Kwapien ideal norms and Hilbertian operators2.4 Ideal norms associated with Hilbert matrices; 3 Ideal norms associated with orthonormal systems; 3.1 Orthonormal systems; 3.2 Khintchine constants; 3.3 Riemann ideal norms; 3.4 Dirichlet ideal norms; 3.5 Orthonormal systems with special properties; 3.6 Tensor products of orthonormal systems; 3.7 Type and cotype ideal norms; 3.8 Characters on compact Abelian groups; 3.9 Discrete orthonormal systems; 3.10 Some universal ideal norms; 3.11 Parseval ideal norms; 4 Rademacher and Gauss ideal norms; 4.1 Rademacher functions
- 4.2 Rademacher type and cotype ideal norms4.3 Operators of Rademacher type; 4.4 B-convexity; 4.5 Operators of Rademacher cotype; 4.6 MP-convexity; 4.7 Gaussian random variables; 4.8 Gauss versus Rademacher; 4.9 Gauss type and cotype ideal norms; 4.10 Operators of Gauss type and cotype; 4.11 Sidon constants; 4.12 The Dirichlet ideal norms 6(#n, ftn) and 6(Sn, Sn); 4.13 Inequalities between 6(Rn, Rn) and g(R,n,J n); 4.14 The vector-valued Rademacher projection; 4.15 Parseval ideal norms and 7-summing operators; 4.16 The Maurey-Pisier theorem; 5 Trigonometric ideal norms
- 5.1 Trigonometric functions5.2 The Dirichlet ideal norms 6(£n, £n); 5.3 Hilbert matrices and trigonometric systems; 5.4 The vector-valued Hilbert transform; 5.5 Fourier type and cotype ideal norms; 5.6 Operators of Fourier type; 5.7 Operators of Fourier cotype; 5.8 The vector-valued Fourier transform; 5.9 Fourier versus Gauss and Rademacher; 6 Walsh ideal norms; 6.1 Walsh functions; 6.2 Walsh type and cotype ideal norms; 6.3 Operators of Walsh type; 6.4 Walsh versus Rademacher; 6.5 Walsh versus Fourier; 7 Haar ideal norms; 7.1 Martingales; 7.2 Dyadic martingales; 7.3 Haar functions
- 7.4 Haar type and cotype ideal norms7.5 Operators of Haar type; 7.6 Super weakly compact operators; 7.7 Martingale type ideal norms; 7.8 J-convexity; 7.9 Uniform g-convexity and uniform p-smoothness; 7.10 Uniform convexity and uniform smoothness; 8 Unconditionality; 8.1 Unconditional Riemann ideal norms; 8.2 Unconditional Dirichlet ideal norms; 8.3 Random unconditionality; 8.4 Fourier unconditionality; 8.5 Haar unconditionality/UMD; 8.6 Random Haar unconditionality; 8.7 The Dirichlet ideal norms (Wn, Wn); 8.8 The Burkholder-Bourgain theorem; 9 Miscellaneous; 9.1 Interpolation