THE SEQUENCE SPACE $\mathcal C(p)$ AND RELATED MATRIX TRANSFORMATIONS

Authors

  • S. Pehlivan University of Akdeniz.
  • Ö. Cakar University of Ankara.

DOI:

https://doi.org/10.5556/j.tkjm.21.1990.4668

Keywords:

Sequence space, Matrix transformations, Incomplete space, Kothe- Toeplitz dual

Abstract

In this paper we define the sequence space $\mathcal C(p)$ defined in an incomplete seminormed space $(X,g)$, namely
\[ \mathcal C(p) = \{(x_k) \subset X: \sup_{r\ge 1}g(x_k - x_{k+r})^{p_k}\to 0, k\to\infty \} \]

where $p =(p_k)$ is a sequence of positive numbers. Then we investigated some of its fundamental properties and some of related matrix transformations.

References

Ö. Cakar, On matrix transformations of sequence spaces defined in an incomplete space, Comm. de la Fae. des Sc. de I 'Universitite d'Ankara, 22 A(l 973), 107-121.

C. G. Lascarides, A study of certain sequence spaces of Maddox a generalization of a theorem of I yer, Pacific J. Math. 38, (1971), 487-500.

I. J. Maddox, Spaces of strongly summable sequences, Quaterly J. Math. Oxford, (2), 18, (1967), 345-355.

I. J. Maddox, Paranormed sequence spaces generated by infiinite matrices, Proc. Camb. Phil. Soc., 64, (1968), 335-340.

I. J. Maddox, Matrix transformations in an incomplete spaces, Canadian J. Math., 20, (1968), 727-734.

M. Stiegliti, Matrix transformationen von unvollstandigen Folgenraumen Math. Z., 133, (1973), 129-132.

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Published

1990-09-01

How to Cite

Pehlivan, S., & Cakar , Ö. . (1990). THE SEQUENCE SPACE $\mathcal C(p)$ AND RELATED MATRIX TRANSFORMATIONS. Tamkang Journal of Mathematics, 21(3), 233–237. https://doi.org/10.5556/j.tkjm.21.1990.4668

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Section

Papers