On modular sequence spaces determined by sequence of Orlicz functions

Year, pages: 2006, 255 - 269

We define a modular sequence space $l(A,{f_n })$ vadjust{vskip-0.5pt}determined by the modular $ρ(x)=∑łimits^∞_n=1∑ łimits^∞_k=1a_nkf_k(|ξ_k|)$, where $x={ξ_k }_n=1^∞$, $A=[a_nk]_{n,k in N}$ is a regular matrix and ${f_n }_n=1^∞$ is a sequence of non-degenerate Orlicz functions. This generalizes the modular spaces considered in [J. Ewert, T. Šalát: Applications of the category method in the theory of modular sequence spaces, Acta Math. Univ. Comenian. XLVIII–XLIX, (1986), 133–143], [J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces. Sequence Spaces I, Springer-Verlag, Berlin, 1977], [J. Musielak: Orlicz Spaces and Modular Spaces, Lecture Notes in Math., Vol. 1034, Springer Verlag, Berlin, 1983], [J. Y. T. Woo: On modular sequence spaces, Studia Math. 48 (1973), 271–289]. We give some properties of such spaces.

Lewandowska, Z. 2006. On modular sequence spaces determined by sequence of Orlicz functions. In Tatra Mountains Mathematical Publications, vol. 34, no.3, pp. 255-269. 1210-3195.

Lewandowska, Z. (2006). On modular sequence spaces determined by sequence of Orlicz functions. Tatra Mountains Mathematical Publications, 34(3), 255-269. 1210-3195.