A new approach to the Dore-Venni theorem

The present paper works out the link between the Dore-Venni theorem and the theory of analytic generators developped by I. CIORANESCU and L. ZSIDO. Th e main result is an inverse theorem: on an UMD-Banach space, analytic gener ators of C-0-groups and operators with bounded imaginary powers are the sam e. The maximal regularity theorem of G. DORE and A. VENNI appears as a coro llary of this fact.