Factorizing Kernel Operators

Abstract

Consider an operator T : X--->Y between Banach function spaces having adequate order continuity and Fatou properties. Assume that T can be factorized through a Banach space as T =SR, where R and the adjoint of S are p-th power and q-th power factorable, respectively. Then a canonical factorization scheme can be given for T. We show that it provides a tool for analyzing T that becomes specially useful for the case of kernel operators. In particular, we show that this square factorization scheme for T is equivalent to some inequalities for the bilinear form defined by T. Kernel operators are studied from this point of view.