Strongly Bounded Partial Sums
DOI:
https://doi.org/10.4067/S0716-09172014000200006Keywords:
Orlicz-Pettis Theorem, locally convex spaces, convergence, teorema de Orlicz-Pettis, espacios localmente convexos, convergencia.Abstract
If λ is a scalar sequence space, a series P Zj in a topological vector space Z is λ multiplier convergent in Z if the series P ∞J =1 tj Zj converges in Z for every t = {tj} ∈ λ-If λ satisfies appropriate conditions, a series in a locally convex space X which is λ multiplier convergent in the weak topology is λ multiplier convergent in the original topology ofthe space (the Orlicz-Pettis Theorem) but may fail to be λ multiplier convergent in the strong topology of the space. However, we show under apprpriate conditions on the multiplier space λ that the series will have strongly bounded partial sums.Downloads
Download data is not yet available.
References
[1] G. Bennett, A New Class of Sequence Spaces with Applications to Summability Theory, J. Reine Angew. Math., 266, pp. 49-75, (1974).
[2] J. Boos, Classical and Modern Methods in Summability, Oxford University Presss, Oxford, (2000).
[3] J. Boos, C. Stuart, C. Swartz, Gliding Hump Properties and Matrix Domains, Analysis Math., 30, pp. 243-257, (2004).
[4] P. K. Kamthan and M. Gupta, Sequence Spaces and Series, Marcel Dekker, N. Y., (1981).
[5] G. Kothe, Topological Vector Spaces I, Springer Verlag, Berlin, (1969).
[6] C. W. McArthur, On a Theorem of Orlicz and Pettis, Pacific J. Math., 22, pp. 297-303, (1967).
[7] D. Noll, Sequential Completeness and Spaces with the Gliding Humps Property, Manuscripta Math., 66, pp. 237-252, (1990).
[8] C. Stuart, Weak Sequential Completeness of β-Duals, Rocky Mountain Math. J., 26, pp. 1559-1568, (1996).
[9] C. Swartz, Multiplier Convergent Series, World Sci. Publ., Singapore, (2009).
[10] C. Swartz, An Abstract Gliding Hump Property, Proy.J. Math., 28, pp. 89-109, (2009).
[11] A. Wilansky, Modern Methods in Topological Vector Spaces, McGrawHill, N. Y., (1978).
[2] J. Boos, Classical and Modern Methods in Summability, Oxford University Presss, Oxford, (2000).
[3] J. Boos, C. Stuart, C. Swartz, Gliding Hump Properties and Matrix Domains, Analysis Math., 30, pp. 243-257, (2004).
[4] P. K. Kamthan and M. Gupta, Sequence Spaces and Series, Marcel Dekker, N. Y., (1981).
[5] G. Kothe, Topological Vector Spaces I, Springer Verlag, Berlin, (1969).
[6] C. W. McArthur, On a Theorem of Orlicz and Pettis, Pacific J. Math., 22, pp. 297-303, (1967).
[7] D. Noll, Sequential Completeness and Spaces with the Gliding Humps Property, Manuscripta Math., 66, pp. 237-252, (1990).
[8] C. Stuart, Weak Sequential Completeness of β-Duals, Rocky Mountain Math. J., 26, pp. 1559-1568, (1996).
[9] C. Swartz, Multiplier Convergent Series, World Sci. Publ., Singapore, (2009).
[10] C. Swartz, An Abstract Gliding Hump Property, Proy.J. Math., 28, pp. 89-109, (2009).
[11] A. Wilansky, Modern Methods in Topological Vector Spaces, McGrawHill, N. Y., (1978).
Downloads
Published
2017-03-23
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]
“Strongly Bounded Partial Sums”, Proyecciones (Antofagasta, On line), vol. 33, no. 2, pp. 205–213, Mar. 2017, doi: 10.4067/S0716-09172014000200006.