Matrix transformations in the sequence spaces L_∞^V(P, S) and C_0^V(P,S)



Abstract

The object of this paper is to obtain necessary and sufficient conditions to characterize the matrices in classes (ly(p,s), l(q)), (c0y(p,s), l(q)), (ly(p,s), c0(q)), and (c0y(p,s), c0(q)) which will fill up a gap in the existing literature.


Keywords

generalized analytic sequence space; matrix-transformations.

1. M. Başarir, On some new sequence spaces and related matrix transformations, Indian J. Pure Appl. Math. 26, 10 (1995), 1003-1010.
2. T. Bilgin, Dual Spaces of Certain sequence spaces, Y.Y.U Journ. of Faculty of Education 1, 2 (1996), 81-88.
3. T. Bilgin, Matrix transformations in the sequence space c_o(p,s) and l_?(p,s), Analele Universitatii din Timisoara, Vol. 36 (1998), 3-12.
4. T. Bilgin, Matrix transformations of some generalized analytic sequence spaces, Math. Comput. Appl. 7, 2 (2002), 165-170.
5. R. Colak, P.D. Srivastava, S. Nanda, On certain sequence spaces and their Köthe-Toeplitz duals, Rendiconti di Matematica, Serie VII, 13 (1993), 27-39.
6. C.G. Lascarides, A study of certain sequence spaces of Maddox and a generalization of a theorem of Iyer, Pacific J. Math. 38, 2 (1971).
7. C.G. Lascarides, I.I. Maddox, Matrix transformations between some classes of sequence spaces, Proc. Camb. Phil. Soc. 68 (1970), 99-104.
8. I.J. Maddox, Spaces of strongly summable sequences, Quaterly J. Math. Oxford (2) 18 (1967), 345-355.
9. I.J. Maddox, Operators on the generalized entire sequences, Proc. Cam. Phil. Soc. 71 (1972), 491-494.
10. J.W. Roles, ph. D. Thesis, University of Lancaster, 1970.
11. S. Simons, The sequence spaces l(p_v) and m(p_v), Proc. London Math. Soc. (3) 15 (1965), 422-436.
12. S.M. Sirajudeen, Inclusion theorem of matrix transformation of some generalized sequence spaces, Soochow J. Math. 7 (1981), 165-174.
13. M.A.I. Willey, On sequence of bounded linear functional with application to matrix transformations, J. Lond. Math. Soc. 7 (2) (1973), 19-30.
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Published : 2003-01-30


BilginT. (2003). Matrix transformations in the sequence spaces L_∞^V(P, S) and C_0^V(P,S). Annales Mathematicae Silesianae, 16, 7-16. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14103

Tunay Bilgin  tbilgin@yyu.edu.tr
Department of Mathematics, Faculty of Education, Yüzüncü Yil University, Turkey  Turkey



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