Journals / Turkish Journal of Mathematics / 2008 / Cilt: 32 - Sayı: 3
On Certain Type of Modular Sequence Spaces
- Pages
- 293–303
- DOI
- —
Abstract
In this paper we consider a particular type of modular sequence spaces defined with the help of a given sequence a = {an} of strictly positive real numbers an's and an Orlicz function M. Indeed, if we define Mn(x) = M(anx) and \tildeMn(x)=M(x/an), x\in[0, \infty), we consider the modular sequence spaces l{Mn} and l{\tildeMn}, denoted by lMa and laM respectively. These are known to be BK-spaces and if M satisfies D2-condition, they are AK-spaces as well. However, if we consider the spaces laM and lna corresponding to two complementary Orlicz functions M and N satisfying D2-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 m and h which contain a and a-1, respectively. We also consider the interrelationship of laM and lMa for different choices of a.
Özet
In this paper we consider a particular type of modular sequence spaces defined with the help of a given sequence a = {an} of strictly positive real numbers an's and an Orlicz function M. Indeed, if we define Mn(x) = M(anx) and \tildeMn(x)=M(x/an), x\in[0, \infty), we consider the modular sequence spaces l{Mn} and l{\tildeMn}, denoted by lMa and laM respectively. These are known to be BK-spaces and if M satisfies D2-condition, they are AK-spaces as well. However, if we consider the spaces laM and lna corresponding to two complementary Orlicz functions M and N satisfying D2-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 m and h which contain a and a-1, respectively. We also consider the interrelationship of laM and lMa for different choices of a.