** Authors:**
MANJUL GUPTA, SHESADEV PRADHAN

** 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
BK-spaces and if M satisfies \Delta_2-condition, they are AK-spaces 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_2-condition, 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

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