Banach spaces of class 𝒮 were
introduced by Fleming and Jamison. This broad class includes all Banach spaces
having hyperorthogonal Schauder bases and, in particular, 𝒮 includes all
Orlicz spaces LΦ on an atomic measure space such that the characteristic
functions of the atoms form a basis for LΦ. The main theorem gives the
structure of one parameter strongly continuous (or (C0)) groups of isometries on
Banach spaces of class 𝒮. Other results correct and complement the work of
Goldstein on groups of isometries on Orlicz spaces over atomic measure
spaces.