  We study closed extensions A of an elliptic differential operator 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-A)^{-1} exists in a sector of the complex plane and decays like
1/|\lambda| as |\lambda| tends to infinity. Moreover, we determine the
structure of the resolvent with enough precision to guarantee existence and
boundedness of imaginary powers of 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.
