# A MATRIX THEOREM AND FURTHER IMPROVEMENT OF THE STILES' SUBSERIES THEOREM

• Yoo, Won-Sok
• Published : 1999.03.01
• 51 4

#### Abstract

In this paper, we obtain a matrix theorem which will be widely used in several theory and give it's applications. In particular, we present a further improvement of the improved Stile's theorem.

#### Keywords

subseries convergence;uniformly convergence;basis

#### References

1. Lecture Notes in Math. v.1113 Matrix Methods in Analysis P. Antosik;C. Swartz
2. Israel J. Math. v.10 Subseries convergence in topological groups and vector measures N. J. Kalton
3. Acta Sci. Math. v.58 A nonlinear Schur Theorem R. Li;C. Swartz
4. Rend. Inst. Matem. v.18 On a theorem of Gelfand and a new proof of the Orlicz-Pettis theorem B. Basit
5. Bull. Soc. Math. Supp. 1. Mem. Unconditional Convergence and the Vitali-Hahn-Saks Theorem A. P. Robertson
6. Ann. Inst. Fourier v.20 L'intergration parrapport a une measure de Radon vectorielle G. Thomas
7. Modern Methods in Topological Vector Spaces A. Wilansky
8. C. R. Acad. Sci. v.274 Sur les suites uniformement convergentes dans un espace de Banach J. Brooks
9. Math. Z. v.163 A generalized Orlicz-Pettis theorem and applications C. Swartz
10. Lecture Notes in Math. v.935 Counterexamples in Topological Vector Spaces S. M. Khaleelulla
11. Contemp. Math. v.2 The Orlicz-Pettis theorem N. J. Kalton
12. Studia Sci. Math, Hungar. v.27 Spaces for which the uniform boundedness principle holds R. Li;C. Swartz
13. Northeastern Math. J. v.11 no.3 An Improvement of Stiles' Orlitcz-Pettis Theorem R. Li;M. H. Cho
14. Israel J. Math. v.8 On subseries convergence in F-spaces W. J. Stiles
15. Rend. Inst. Matem. v.20 A generalization of Stiles' Orlicz-Pettis theorem C. Swartz