Bases of complemented subspaces of functional spaces (Q756658)

Let (X,m) be a measure space and let \((a_ r)^{\infty}_{r=1}\) be a sequence of nonnegative measurable functions on X. By \(L_ 2(a_ r)\) we shall denote weighted \(L_ 2\)-space. Let E be a projective limit of \(L_ 2(a_ r)\) with respect to natural embeddings. Sufficient conditions for complemented subspaces of E to have unconditional bases are obtained.