Uniform boundedness in vector-valued sequence spaces
DOI:
https://doi.org/10.4067/S0716-09172004000300003Keywords:
Scalar spaces, K-spaces, locally convex space, espacios escalares, K-espacios, espacio localmente convexo.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 x = {xk} such that {q(x?)} ? µ{X} for all q ? X. The space µ{X} is given the locally convex topology generated by the semi-norms ?pq(x) = p({q(x?)}), p ? X, q ? M.We show that if µ satisfies a certain multiplier type of gliding hump property, then pointwise bounded subsets of the ?-dual of µ{X} with respect to a locally convex space are uniformly bounded on bounded subsets of µ{X}.
Downloads
Download data is not yet available.
References
[1] J. Boos and T. Leiger, Some distinguished subspaces of domains of operator valued matrices, Results Math., 16, pp. 199-211, (1989).
[2] M. Florencio and P. Paul, Barrelledness conditions on certain vector valued sequence spaces, Arch. Math., 48, pp. 153-164, (1987).
[3] J. Fourie, Barrelledness Conditions on Generalized Sequence Spaces, South African J. Sci., 84, pp. 346-348, (1988).
[4] A. Pietsch, Verallgemeinerte vollkommene Folgenraume, Schrift. Inst. Math., Deutsch Akad. Wiss. Berlin, Heft 12, Acad. Verlag, Berlin, (1962).
[5] R. Rosier, Dual Spaces of Certain Vector Sequence Spaces, Pacific J. Math., 46, pp. 487-501, (1973).
[6] C. Swartz, Introduction to Functional Analysis, Marcel Dekkar, N. Y., (1992).
[7] C. Swartz, Infinite Matrices and the Gliding Hump, World. Sci. Publ., Singapore, (1996).
[8] C. Swartz, A Multiplier Gliding hump Property for Sequence Spaces, Proyecciones Revista de Matemática, Vol. 20, pp. 19-31, (2001).
[9] A. Wilansky, Modern Methods in Topological Vector Spaces, McGrawHill, N. Y., (1978).
[2] M. Florencio and P. Paul, Barrelledness conditions on certain vector valued sequence spaces, Arch. Math., 48, pp. 153-164, (1987).
[3] J. Fourie, Barrelledness Conditions on Generalized Sequence Spaces, South African J. Sci., 84, pp. 346-348, (1988).
[4] A. Pietsch, Verallgemeinerte vollkommene Folgenraume, Schrift. Inst. Math., Deutsch Akad. Wiss. Berlin, Heft 12, Acad. Verlag, Berlin, (1962).
[5] R. Rosier, Dual Spaces of Certain Vector Sequence Spaces, Pacific J. Math., 46, pp. 487-501, (1973).
[6] C. Swartz, Introduction to Functional Analysis, Marcel Dekkar, N. Y., (1992).
[7] C. Swartz, Infinite Matrices and the Gliding Hump, World. Sci. Publ., Singapore, (1996).
[8] C. Swartz, A Multiplier Gliding hump Property for Sequence Spaces, Proyecciones Revista de Matemática, Vol. 20, pp. 19-31, (2001).
[9] A. Wilansky, Modern Methods in Topological Vector Spaces, McGrawHill, N. Y., (1978).
Downloads
Published
2017-05-22
Issue
Section
Artículos
License
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
How to Cite
[1]
“Uniform boundedness in vector-valued sequence spaces”, Proyecciones (Antofagasta, On line), vol. 23, no. 3, pp. 235–240, May 2017, doi: 10.4067/S0716-09172004000300003.
