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Proyecciones (Antofagasta)
versión impresa ISSN 0716-0917
Proyecciones (Antofagasta) v.23 n.3 Antofagasta dic. 2004
http://dx.doi.org/10.4067/S0716-09172004000300003
| Proyecciones UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES
CHARLES SWARTZ New Mexico State University, USA ABSTRACT 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}. References [1] J. Boos and T. Leiger, Some distinguished subspaces of domains of operator valued matrices, Results Math., 16, pp. 199-211, (1989). [ Links ] [2] M. Florencio and P. Paul, Barrelledness conditions on certain vector valued sequence spaces, Arch. Math., 48, pp. 153-164, (1987). [ Links ] [3] J. Fourie, Barrelledness Conditions on Generalized Sequence Spaces, South African J. Sci., 84, pp. 346-348, (1988). [ Links ] [4] A. Pietsch, Verallgemeinerte vollkommene Folgenraume, Schrift. Inst. Math., Deutsch Akad. Wiss. Berlin, Heft 12, Acad. Verlag, Berlin, (1962). [ Links ] [5] R. Rosier, Dual Spaces of Certain Vector Sequence Spaces, Pacific J. Math., 46, pp. 487-501, (1973). [ Links ] [6] C. Swartz, Introduction to Functional Analysis, Marcel Dekkar, N. Y., (1992). [ Links ] [7] C. Swartz, Infinite Matrices and the Gliding Hump, World. Sci. Publ., Singapore, (1996). [ Links ] [8] C. Swartz, A Multiplier Gliding hump Property for Sequence Spaces, Proyecciones Revista de Matemática, Vol. 20, pp. 19-31, (2001). [ Links ] [9] A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, N. Y., (1978). [ Links ] Received : July 2004. Accepted : November 2004 Charles Swartz
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