SOME TOPOLOGICAL STRUCTURES OF NORMED SPACE VALUED ORLICZ FUNCTION SPACE ( l∞ (U, V, || . ||, Ω ))

Abstract

The aim of this work is to study new classes  l∞  (U, V, || . ||,  Ω ) and l∞(U, V, || . ||,  Ω, λ) of normed space valued  function space using Orlicz function Ω  as the generalizations of well known complex basic sequence space  l∞ studied in Functional Analysis.  These results can be used for further generalization to investigate the various properties of  existing Orlicz function  spaces. Besides the investigation of  linear topological structures of  the class l∞  (U, V, || . ||,  Ω ) when topologized it with suitable natural norm, our primarily interest is to explore the various conditions pertaining to  the  inclusion  of the class  l∞(U, V, || . ||,  Ω, λ) in terms of different values of  λ.when topologized it with suitable natural norm, our primarily interest is to explore the various conditions pertaining to  the  inclusion  of the class