We deduce one-parameter group properties for pseudo-differential operators Op(a), where a belongs to the class Γ (ω 0 ) * of certain Gevrey symbols. We use this to show that there are pseudo-differential operators Op(a) and Op(b) which are inverses to each others, where a ∈ ΓWe apply these results to deduce lifting property for modulation spaces and construct explicit isomorpisms between them. For each weight functions ω, ω 0 moderated by GRS submultiplicative weights, we prove that the Toeplitz operator (or localization operator) Tp(ω 0 ) is an isomorphism from M p,q(ω) onto M p,q(ω/ω 0 ) for every p, q ∈ (0, ∞].