Sequence Space (sl(p)) Generated by an Infinite Diagonal Matrix

Shailendra K. Mishra; Vinod Parajuli; Suresh Ray

doi:https://doi.org/10.14445/22315373/IJMTT-V18P511

International Journal of Mathematics Trends and Technology

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Volume 18 | Number 2 | Year 2015 | Article Id. IJMTT-V18P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V18P511

Sequence Space (sl(p)) Generated by an Infinite Diagonal Matrix

Shailendra K. Mishra, Vinod Parajuli, Suresh Ray

Abstract

The sequence space (l(p)) = {x=(xk) ∶ ∑k=1∞tk(x)pk < ∞ } where tk(x)=∑i=1k xiwas introduced and studied by B. Choudhary and S.K. Mishra [3]. In the present paper, we generalize the space (l(p)) by means of an infinite diagonal matrix A=(ank )={0(2-n) & for n=k otherwise and introduce a new sequence space (sl(p)). We shall study some properties of (sl(p)) and find its β- dual. Furthermore we characterize the matrix classes ((sl(p) ),l∞) and ((sl(p)),c).

Keywords

Paranormed sequence space, β- dual , Matrix transformation

References

[1] B. Atlay, F. Basar , E. Malkowsky , Matrix transformation on some sequence spaces related to strong Cesaro summability and boundedness, Applied Mathematics and Computation 211 (2009) 255-264
[2] B. Atlay, F. Basar , On the paranormed Riesz Sequence spaces of non-absolute type, Southeast Asian Bull. Math. 26 (2002) 701-715
[3] B. Choudhary and S. K. Mishra, On Kothe- Toeplitz Duals of certain Sequence spaces and their matrix transformations, Indian Journal of Pure Appl. Mathematics , 24(5) May 1993
[4] B. Choudhary and S. K. Mishra , A note on Kothe- Toeplitz Duals of certain Sequence spaces and their matrix transformations, International Journal of Mathematical Science (18) , 1995 , No. 4, 681-688
[5] E. Malkowsky, E.Savas, Matrix transformation between sequence spaces of generalized weighted means, Appl. Math. Comput. 147 (2004) 333-345
[6] E. Malkowsky , V. Rakocevic, Snezana Zivkovic, Matrix Transformation Between The Sequence Space BVp And Certain BK Spaces, Bulletin T.CXXIII de l’ Academie Serbe des Science et des Arts- 2002, No. 27 (34-46)
[7] H. Kizmaz , On certain sequence spaces , Canad. Math. Bull. , 24(2) (1981), 169-176
[8] E. Kreyszig, Introductory Functional Analysis With Applications, New York; John Wiley and Sons, 1978.
[9] Kuldip Raj and Sunil K. Sharma , Some Multiplier Sequence Spaces Defined By A Musielak- Orlicz Functions In n- Normed Spaces, New Zealand Journal of Mathematics , vol 42 (2012), 45-56.
[10] I.J. Maddox, Elements of Functional Analysis, Cambridge University Press , 1988.
[11] S. K. Mishra, Sequence Spaces and Related Topics, PhD Thesis, Indian Institute of Technology, Delhi,November, 1993

Citation :

Shailendra K. Mishra, Vinod Parajuli, Suresh Ray, "Sequence Space (sl(p)) Generated by an Infinite Diagonal Matrix," International Journal of Mathematics Trends and Technology (IJMTT), vol. 18, no. 2, pp. 65-73, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V18P511