Abstract

Given a bounded, non-negative operator W and a projection P on a Hilbert space, we find necessary and suficient conditions for the existence of a non-trivial, non-negative operator V such that P is bounded from L²(W) to L²(V ). This leads to a vector-valued version of a theorem of Koosis and Treil’ concerning the boundedness of the Riesz projection in spaces with weights.

Authors