Factorizing Kernel Operators

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.Support of the Ministerio de Economia y Competitividad under project # MTM2012-36740-C02-02 (Spain) is gratefully acknowledged.Galdames, O.; Sánchez Pérez, EA. (2013). Factorizing Kernel Operators. Integral Equations and Operator Theory. 75(1):13-29. doi:10.1007/s00020-012-2019-zS132975