Orlicz-Pettis theorems for multiplier convergent operator valued series

  • Charles Swartz New Mexico State University.
Palabras clave: Locally convex spaces, Orlicz-Pettis theorems, continuous linear operators, convergence, scalar spaces, sequence spaces, series, locally convex topology, espacios localmente convexos, teoremas de Orlicz-Pettis, operadores lineales continuos, convergencia.


Let X, Y be locally convex spaces and L(X, Y ) the space of continuous linear operators from X into Y . We consider 2 types of multiplier convergent theorems for a series ∑ Tₕ in L(X, Y ). First, if λ is a scalar sequence space, we say that the series ∑ Tₕ is λ multiplier P convergent for a locally convex topology τ on L(X, Y ) if the series ∑ tₕTₕ is τ convergent for every t = {tₕ} ∈ λ. We establish conditions on λ which guarantee that a λ multiplier convergent series in the weak or strong operator topology is λ multiplier convergent in the topology of uniform convergence on the bounded subsets of X. Second, we consider vector valued multipliers. If E is a sequence space of X valued sequences, the series ∑ Tₕ is E multiplier convergent in a locally convex topology η on Y if the series ∑ Tₕxₕ is η convergent for every x = {xₕ} ∈ E. We consider a gliding hump property on E which guarantees that a series ∑ Tₕ which is E multiplier convergent for the weak topology of Y is E multiplier convergent for the strong topology of Y .

Biografía del autor/a

Charles Swartz, New Mexico State University.
Mathematics Department.


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Cómo citar
Swartz, C. (2017). Orlicz-Pettis theorems for multiplier convergent operator valued series. Proyecciones. Revista De Matemática, 23(1), 61-72. https://doi.org/10.4067/S0716-09172004000100005