The resolvent of closed extensions of cone differential operators

We study closed extensions \underline{A} of an elliptic differential operator A on a manifold with conical singularities, acting as an unbounded operator on a weighted L_p-space. Under suitable conditions we show that the resolvent (\lambda-\underline A)^{-1} exists in a sector of the complex plane and decays like 1/|\lambda| as |\lambda|\to\infty. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of \underline{A}. As an application we treat the Laplace-Beltrami operator for a metric with straight conical degeneracy and describe domains yielding maximal regularity for the Cauchy problem \dot{u}-\Delta u=f, u(0)=0.