Gliding Hump Properties in Abstract Duality Pairs with Projections

  • Charles Swartz New Mexico State University.
Palabras clave: Topological vector spaces, bounded sets, convergent series, espacios vectoriales topológicos, conjuntos acotados, series convergentes.

Resumen

Let E, G be Hausdorff topological vector spaces and let F be a vector space. Assume there is a bilinear operator <.,.> : E X F →G such that <.,y> : 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 ofE and pointwise bounded subsets of F. Under additional gliding hump assumptions, uniform convergent results are established for series ∑ ∞ j=1 < Pjx,y> 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.

Biografía del autor/a

Charles Swartz, New Mexico State University.
Mathematics Department.

Citas

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Publicado
2017-03-23
Cómo citar
Swartz, C. (2017). Gliding Hump Properties in Abstract Duality Pairs with Projections. Proyecciones. Journal of Mathematics, 35(3), 339-367. https://doi.org/10.4067/S0716-09172016000300009
Sección
Artículos