New Paranormed Sequence Spaces l∞(p,λ) , c(p,λ) and c0(p,λ) Generated by an Infinite Matrix

Shailendra K. Mishra; Vinod Parajuli; Sergei Silvestrov

doi:https://doi.org/10.14445/22315373/IJMTT-V6P516

International Journal of Mathematics Trends and Technology

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Volume 6 | Number 2 | Year 2014 | Article Id. IJMTT-V6P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V6P516

New Paranormed Sequence Spaces l∞(p,λ) , c(p,λ) and c0(p,λ) Generated by an Infinite Matrix

Shailendra K. Mishra , Vinod Parajuli , Sergei Silvestrov

Citation :

Shailendra K. Mishra , Vinod Parajuli , Sergei Silvestrov, "New Paranormed Sequence Spaces l∞(p,λ) , c(p,λ) and c0(p,λ) Generated by an Infinite Matrix," International Journal of Mathematics Trends and Technology (IJMTT), vol. 6, no. 2, pp. 176-182, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V6P516

Abstract

In this paper we introduce a set of new paranormed sequence spaces l p  ( , )  , c p( , )  and 0 c p( , )  which are generated by an infinite lower uni triangular matrix n  S where ( ) nk S s  is an infinite matrix given by, 1; 0 ( ) 0; nk k n S s k n        as defined in [6] . We also compute the basis for the spaces c p( , )  and 0 c p( , )  , obtain β – dual for all these spaces and characterize the matrix classes l p l   ( , ),   ,l p c  ( , ),   and l p c  ( , ),  0 .

Keywords

Paranormed sequence spaces, β – dual, matrix transformation

References

[1] I.J. Maddox, “Paranormed sequence spaces generated by infinite matrices”, Proc. Cambridge Philos. Soc., 64 , pp.335-340, 1968
[2] I.J. Maddox, “Spaces of Strongly summable sequences”, Quart. J. Math. Oxford (2) ,18, pp. 345-355, 1967
[3] C.G. Lascarides and I.J. Maddox, “Matrix transformation between some classes of sequences”, Proc. Cambridge Philos. Soc., 68, pp. 99-104, 1970
[4] I.J. Maddox, “Some properties of paranormed sequence spaces”, London J. Math. Soc.(2), 1 , pp. 316-322 , 1969
[5] S. Simons , “The sequence spaces l(pν)and m(pν)”, Proc. Lond. Math. Soc(3), 15 , pp. 422-436, 1965
[6] B. Choudhary and S.K. Mishra, “On Kothe-Toeplitz duals of certain sequence spaces and their matrix transformations”, Indian J. Pure Appl. Math 24(5), pp. 291-301 , 1993
[7] P. Baliarsingh, “A set of new paranormed difference sequence spaces and their matrix transformations”, Asian-European J.of Math. , vol.6, No. 3 , pp .1350040(1)-1350040(12) , 2013
[8] I.J. Maddox, Elements of Functional Analysis, 2nd ed, Cambridge University Press, 1970.