Dual and perfect sequence and function space

Abstract

In this work we develop the study of sequence spaces and dual space of sequence spaces, by establishing some of the results. We also extend our study by establishing a few results in the case of function spaces and dual space of function space analogous to that for sequence spaces. Our effort in this paper is to make a comparative study of sequence and function spaces by proving some results. In the course of establishing some of the results we observed that by changing the technical results we can also establish the results for function spaces analogous to that for sequence spaces. The reason behind this is that in the study of sequences  and sequence  spaces  we  deal with positive  integers  whereas  in the  study  of functions and function spaces we play with variables. From the theorems established in this paper   it  is  clear  that  the  behaviors  of some  of the  sequence  and  function spaces  are almost identical although their methods of proofs differ.