Projections in weighted spaces,skew projections and inversion of Toeplitz operators

In many cases the self-adjoint projection of a Lebesgue space L²(dx) onto a closed subspace is also bounded on a weighted space L²(wdx) . Our main result is that in this case certain self-adjoint projections on weighted spaces are bounded on L²(dx) . The analysis also produces an invertibility criterion for certain Toeplitz operators. The proof is based on analysis of a perturbation series and hence is valid in fairly general circumstances.Both authors supported in part by grants from the National Science Foundation.