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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Resumen

SWARTZ, CHARLES. UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES. Proyecciones (Antofagasta) [online]. 2004, vol.23, n.3, pp.235-240. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172004000300003.

Let µ be a normal scalar sequence space which is a K-space under the family of semi-norms M and let X be a locally convex space whose topology is generated by the family of semi-norms X. The space µ{X} is the space of all X valued sequences c = {ck} such that {q(ck)} ε{X} for all q Î X. The space µ{X} is given the locally convex topology generated by the semi-norms ðppq(c) = p({q(ck)}), p Î X, q Î M. We show that if µ satisfies a certain multiplier type of gliding hump property, then pointwise bounded subsets of the â-dual of µ{X} with respect to a locally convex space are uniformly bounded on bounded subsets of µ{X}

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