The Banach-Steinhaus Theorem in Abstract Duality Pairs

  • Li Ronglu Harbin Institute of Technology.
  • Charles Swartz New Mexico State University.
Palabras clave: Matemáticas.

Resumen

Let E, F be sets and G a Hausdorff, abelian topological group with b : E X F→ G; we refer to E, F, G as an abstract duality pair with respect to G or an abstract triple and denote this by (E,F : G). Let (Ei,Fi : G) be abstract triples for i = 1, 2. Let Fi be a family of subsets of    Fi    and let    τFi(Ei)    =    τibe    the    topology on    Ei   of uniform convergence on the members of Fi. Let J be a family of mappings from Ei to E2. We consider conditions which guarantee that J is τ1-τ2equicontinuous. We then apply the results to obtain versions of the Banach-Steinhaus Theorem for both abstract triples and for linear operators between locally convex spaces.

Biografía del autor

Li Ronglu, Harbin Institute of Technology.
Department of Mathematics.
Charles Swartz, New Mexico State University.
Department of Mathematical Sciences.

Citas

[CLS] M. Cho, R. Li and C. Swartz, Subseries convergence in abstract duality pairs, Proy. J. Math., 33, pp. 447-470, (2014).

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Cómo citar
[1]
L. Ronglu y C. Swartz, The Banach-Steinhaus Theorem in Abstract Duality Pairs, PJM, vol. 34, n.º 4, pp. 391-399, 1.
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