In this paper, we study multivalued linear operators (MLO’s) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the HilleYosida condition. Then we describe the generalized semigroups induced by MLO’s. We present a criterion for an MLO to be a generator The work of A. Baskakov and V. Obukhovskii is partially support...