On Vector-Valued Operator Riesz Sequence Spaces

Abstract

In this paper we introduce vector-valued Riesz sequence spaces R₀^{q}(X), R_{c}^{q}(X), R_{∞}^{q}(X) and R₁^{q}(X) and determine their Köthe-Toeplitz duals. Also, we characterize some matrix classes.

Keywords

• Vector-valued sequence spaces,Köthe-Toeplitz dual,matrix transformations

References

1. Lorentz, G. G. and Machphail, M. S., Unbounded operators and a theorem of A. Robinson, Trans. Royal Soc. of C XLVI, (1952), 33-37.
2. Robinson, A.R., On functional transformations and summability, Proc. London Math. Soc., 52, (1995), 132-160.
3. Maddox, I. J., Infinite matrices of operators, Lecture notes in Mathematics, 786 Springer-Verlag, Berlin.
4. Maddox, I. J., Spaces of strongly summable sequences, The Quarterly Journal of Mathematics, 18(1), (1967), 345-53.
5. Nappus, A. and Sõrmus, T., Einige verallgemeinerte matrixverfahren, Proc. Estonian Acad. Sci. Phys.Math., 45(2-3), (1996), 201-210.
6. Aasma, A., Matrix transformations of summability domains of generalized matrix methods in Banach spaces, Rendiconti del Circolo Matematico di Palermo, 58, (2009), 467-476 .
7. Malkowsky, E. and Rakočević, V., Measure of noncompactness of linear operators between spaces of sequences that are (N,q) summable or bounded, Czechoslovak Mathematical Journal, 51, (126), (2001), 505-522.
8. Şengönül, M. and Başar, F., Some new Cesàro sequence spaces of non-absolute type which include the spaces c₀ and c, Soochow Journal of Mathematics, 31(1), (2005), 107-119.

9. Altay, B. and Başar, F., On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bulletin of Mathematics, 24(2), (2003), 701-715.
10. Altay, B. and Başar, F., Some paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bulletin of Mathematics, 30(4), (2006), 591-608.
11. Altay, B. and Başar, F., Some Euler sequence spaces of non-absolute type, Ukrainian Mathematical Journal, 57(2), (2005), 1-17.