Weak* topology on modular space and some properties

Abstract

This study aims to redefine the weak topology on σ ( X M * , X M * * ) on a specific topological dual space (modular dual space XM * ) this is weak topology generated by all linear bounded functional on XM * , but we interested in a subspace of this topology generated by XM called weak* topology on XM * , it follows from that the modular space XM over the field K can be embedded in X M * * by using the canonical map, we denoted to this topology by σ ( X M * , X M ) . After that, we checked the weak* topology is Hausdorff and investigated some properties, finally, we showed that under which condition the strong topology and the weak* topology coincided.