Multiplication operators in Kothe-Bochner spaces

Let X be a Banach space and E an order continuous Banach function space over a finite measure mu. We prove that an operator T in the Kothe-Bochner space E(X) is a multiplication operator (by a function in L(infinity)(mu)) if and only if the equality T(g x) = g x holds for every g is an element of L(infinity)(mu), f is an element of E(X), x is an element of X and x* is an element of X*. (C) 2010 Elsevier Inc.J.M. Calabuig was supported by MEC and FEDER (project MTM2008-04594) and Generalitat Valenciana (project GV/2009/102). J. Rodriguez was supported by MEC and FEDER (project MTM2008-05396) and Fundacion Seneca (project 08848/PI/08). E.A. Sanchez-Perez was supported by MEC and FEDER (project MTM2009-14483-C02-02). The authors were also supported by Universidad Politecnica de Valencia (project PAID-06-08-3093).Calabuig Rodriguez, JM.; Rodriguez, J.; Sánchez Pérez, EA. (2011). Multiplication operators in Kothe-Bochner spaces. Journal of Mathematical Analysis and Applications. 1(373):316-321. https://doi.org/10.1016/j.jmaa.2010.07.038S316321137