Existence of optimal subspaces in reflexive Banach spaces
| Autor: | Fabián Eduardo Levis, Hector H. Cuenya |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Control and Optimization Matemáticas Eberlein–Šmulian theorem Banach space reflexive Banach space Banach manifold Tsirelson space Matemática Pura Pseudo-monotone operator 41A65 OPTIMAL SUBSPACES Mathematics Discrete mathematics Algebra and Number Theory 41A28 existence Uniformly convex space Reflexive operator algebra EXISTENCE Optimal subspaces 46B28 Reflexive space REFLEXIVE BANACH SPACE CIENCIAS NATURALES Y EXACTAS Analysis |
| Zdroj: | Ann. Funct. Anal. 6, no. 2 (2015), 69-77 |
| ISSN: | 2008-8752 |
| DOI: | 10.15352/afa/06-2-7 |
| Popis: | Given a finite set Y in a reflexive Banach space F and a family C of closed subspaces of F, we study the problem of finding a subspace W in C that best approximates the data Y in the sense that sum_{f in Y} d(f,W) = min_{V in C} sum_{f in Y} d(f,V), where d is the distance function on F. In this paper, we give necessary conditions and sufficient conditions over C for which such a best approximation exists. In particular, when F has finite dimension a characterization on C is given. Fil: Cuenya, Hector Hugo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina Fil: Levis, Fabián Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina |
| Databáze: | OpenAIRE |
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