Gliding Hump Properties in Abstract Duality Pairs with Projections



Título del documento: Gliding Hump Properties in Abstract Duality Pairs with Projections
Revista: Proyecciones (Antofagasta)
Base de datos: PERIÓDICA
Número de sistema: 000406116
ISSN: 0716-0917
Autores: 1
Instituciones: 1New Mexico State University, Mathematics Department, Las Cruces, Nuevo México. Estados Unidos de América
Año:
Periodo: Sep
Volumen: 35
Número: 3
Paginación: 339-367
País: Chile
Idioma: Inglés
Tipo de documento: Artículo
Enfoque: Analítico
Resumen en inglés Let E,G be Hausdorff topological vector spaces and let F be a vector space. Assume there is a bilinear operator h·, ·i : E × F → G such that h·, yi : E → G is continuous for every y ∈ F. The triple E, F, G is called an abstract duality pair with respect to G or an abstract triple and is denoted by (E,F : G). If {Pj} is a sequence of continuous projections on E, then (E,F : G) is called an abstract triple with projections. Under appropriate gliding hump assumptions, a uniform bounded principle is established for bounded subsets of E and pointwise bounded subsets of F. Under additional gliding hump assumptions, uniform convergent results are established for series P∞ j=1 hPjx, yi when x varies over certain subsets of E and y varies over certain subsets of F. These results are used to establish uniform countable additivity results for bounded sets of indefinite vector valued integrals and bounded subsets of vector valued measures
Disciplinas: Matemáticas
Palabras clave: Matemáticas aplicadas,
Matemáticas puras,
Espacios de sucesiones,
Espacios vectoriales topológicos,
Sucesiones
Keyword: Mathematics,
Applied mathematics,
Pure mathematics,
Sequence spaces,
Topological vector spaces,
Sequences
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