Reflexivity of the group of subjective isometries on some Banach spaces

In this paper we study the problem of algebraic reflexivity of the isometry group of some important Banach spaces. Because of the previous work in sim ilar topics, our main interest lies in the von Neumann - Schatten p-classes of compact operators. The ideas developed there can be used in l(p)-spaces , Banach spaces of continuous functions and spin factors as well. Moreover, we attempt to attract the attention to this problem from general Banach sp aces geometry view-point. This study, we believe, would provide nice geomet rical results.