L^pspectra of pseudodifferential operators generating integrated semigroups

Consider the L^p-realization Op_p(a) of a pseudodifferential operator with symbol a ϵs^m _{p, 0}having constant coefficients. We show that for a certain class of symbols the spectrum of Op_p(a) is independent of p. This implies that Op_p(a) generates an TV-times integrated semigroup on W(W) for a certain N if and only if pOp_p(a)≠ ∅ and the numerical range of a is contained in a left half-plane. Our method allows us also to construct examples of operators generating integrated semigroups on L^p(Rⁿ) if and only if p is sufficiently close to 2.