International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 5, Pages 295-304
doi:10.1155/S0161171203111325

Characterizations of vector-valued weakly almost periodic functions

Abstract

We characterize the weak almost periodicity of a vector-valued, bounded, continuous function. We show that if the range of the function is relatively weakly compact, then the relative weak compactness of its right orbit is equivalent to that of its left orbit. At the same time, we give the function some other equivalent properties.