Special factorization of a noninvertible Fredholm operator of the second kind (Q1779901)

Let \(K\) be an integral operator in a functional Banach space and \(I-K\) be noninvertible. The author investigates the factorization of the form \( I-K=W_{+}(I-K_{1})W_{-} \), where \(W_{+}\) (\(W_{-}\)) is a left (right) invertible operator and \(I-K_{1}\) is invertible in appropriately defined functional spaces. The paper gives the solution of this problem for the spaces \(L_{p}(0,1)\) (\(1<p<\infty\)) when \(K\) is an integral operator with a bounded kernel.