Characterizations of a class of matrix transformations
DOI:
https://doi.org/10.22199/S07160917.1998.0001.00001Keywords:
Matrix Transformation, Sequence space, ω0 - WGHPAbstract
One of the important investigations in the theory of summability is that of finding characterizations on an infinite matrix in order that the matrix should transform one sequence into another sequence space. In this note we present an abstract matrix transformation theorem. Prom it we can obtain the characterizations of a class of matrix transformations.
References
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2. J. Batt, Applications of the Orlics-Pettis theorem to operator-valued measures and compact and weakly compact linear transformations on the space of continuous functions, Revue. Roum. Math. Pures Appl. 14, pp. 907- 945, (1969).
3. C. Bessaga and A. Pelczynski, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17, pp. 151 - 164, (1958).
4. D. J. H. Garling, On topological sequence spaces, Proc. Camb. Phil. Soc. 63, pp. 997- 1019, (1967).
5. Li Ronglu and Bu Qingying, Locally convex space containing no copy of co, J. Math. Anal. Appl. 172, pp. 205-211, (1993).
6. Li Ronglu and Cho Minhyung, Bounded multiplier convergent series and applications, Bull. Korean Math. Soc. 29, pp. 215-220, (1992).
7. Li Ronglu and C. Swartz, Spaces for which the uniform boundedness principle holds, Sudia Sci. Math. Hung. 27, pp. 379- 384, (1992).
8. Li Ronglu and C. Swartz, A nonlinear Schur theorem, Acta Sci. Math. (Szeged) 58, pp. 497- 508, (1993).
9. I. Maddox, Schur's theorem for operators, Bull. Soc. Math. Crece 16, pp. 18-21, (1975).
10. Maddox, Infinite matrices of operators, Springer Lecture Notes in Mathematics 786, Heidelberg, (1980).
11. D. Noll, Sequential completeness and spaces with the gliding humps property, Manuscripta Math. 66, pp. 237- 252, (1990).
12. R. Rolewicz, Matric linear spaces, Polish Sci. Publ., Warsaw, (1972).
13. C. Swartz, The Schur lemma for bounded multiplier convergent series, Math. Ann. 263, pp. 283-288, (1983).
14. C. Swartz, The Schur lemma and Hahn Theorems for operators matrices, Rocky Mountain J. Math. 15, pp. 61 - 73, (1985).
15. C. Swartz, The gliding hump property in vector sequence spaces, Monatsh. fur Math. 116, pp. 147- 158, (1993).
16. C. Swartz, Infinite Matrices and the Gliding Hump, World Sci. Publ., Singapore, (1996).
17. B. L. D. Thorp, Sequential-evaluation convergence, J. London Math. Soc. 44, pp. 201 - 209, (1969).
2. J. Batt, Applications of the Orlics-Pettis theorem to operator-valued measures and compact and weakly compact linear transformations on the space of continuous functions, Revue. Roum. Math. Pures Appl. 14, pp. 907- 945, (1969).
3. C. Bessaga and A. Pelczynski, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17, pp. 151 - 164, (1958).
4. D. J. H. Garling, On topological sequence spaces, Proc. Camb. Phil. Soc. 63, pp. 997- 1019, (1967).
5. Li Ronglu and Bu Qingying, Locally convex space containing no copy of co, J. Math. Anal. Appl. 172, pp. 205-211, (1993).
6. Li Ronglu and Cho Minhyung, Bounded multiplier convergent series and applications, Bull. Korean Math. Soc. 29, pp. 215-220, (1992).
7. Li Ronglu and C. Swartz, Spaces for which the uniform boundedness principle holds, Sudia Sci. Math. Hung. 27, pp. 379- 384, (1992).
8. Li Ronglu and C. Swartz, A nonlinear Schur theorem, Acta Sci. Math. (Szeged) 58, pp. 497- 508, (1993).
9. I. Maddox, Schur's theorem for operators, Bull. Soc. Math. Crece 16, pp. 18-21, (1975).
10. Maddox, Infinite matrices of operators, Springer Lecture Notes in Mathematics 786, Heidelberg, (1980).
11. D. Noll, Sequential completeness and spaces with the gliding humps property, Manuscripta Math. 66, pp. 237- 252, (1990).
12. R. Rolewicz, Matric linear spaces, Polish Sci. Publ., Warsaw, (1972).
13. C. Swartz, The Schur lemma for bounded multiplier convergent series, Math. Ann. 263, pp. 283-288, (1983).
14. C. Swartz, The Schur lemma and Hahn Theorems for operators matrices, Rocky Mountain J. Math. 15, pp. 61 - 73, (1985).
15. C. Swartz, The gliding hump property in vector sequence spaces, Monatsh. fur Math. 116, pp. 147- 158, (1993).
16. C. Swartz, Infinite Matrices and the Gliding Hump, World Sci. Publ., Singapore, (1996).
17. B. L. D. Thorp, Sequential-evaluation convergence, J. London Math. Soc. 44, pp. 201 - 209, (1969).
Published
2018-04-04
How to Cite
[1]
W. Junde, C. Wei, and L. Ronglu, “Characterizations of a class of matrix transformations”, Proyecciones (Antofagasta, On line), vol. 17, no. 1, pp. 1-11, Apr. 2018.
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