Turkish Journal of Mathematics
DOI

Abstract
In this paper we consider a particular type of modular sequence spaces defined with the help of a given sequence \alpha = {\alpha_n} of strictly positive real numbers \alpha_n's and an Orlicz function M. Indeed, if we define M_n(x) = M(\alpha_nx) and \tildeM_n(x)=M(x/\alpha_n), x\in[0, \infty), we consider the modular sequence spaces l{M_n} and l{\tildeM_n}, denoted by l_M^{\alpha} and l_{\alpha}^M respectively. These are known to be BKspaces and if M satisfies \Delta_2condition, they are AKspaces as well. However, if we consider the spaces l_{\alpha}^M and l_n^{\alpha} corresponding to two complementary Orlicz functions M and N satisfying \Delta_2condition, they are perfect sequence spaces, each being the Köthe dual of the other. We show that these are subspaces of the normal sequence spaces \mu and \eta which contain \alpha and \alpha^{1}, respectively. We also consider the interrelationship of l_{\alpha}^M and l_M^{\alpha} for different choices of \alpha.
Keywords
Orlicz functions, Modular sequence spaces, Köthe dual
First Page
293
Last Page
303
Recommended Citation
GUPTA, MANJUL and PRADHAN, SHESADEV (2008) "On Certain Type of Modular Sequence Spaces," Turkish Journal of Mathematics: Vol. 32: No. 3, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol32/iss3/4