Order bidual of f-algebras and a-linear operators on Banach A-modules

In this thesis, order bidual of f-algebra A and linear operators on Banach A-modules are investigated. Let X be an Archimedean f-algebra. The Arens multiplication in the order bidual X'' is given. With this multiplication it is shown that the mapping , for and the mapping are algebra homomorphism, where , . Let be a Banach f-algebra. The definition of linear operator on Banach modul is given. Let and be a Banach modul. It is shown that and are Banach modul. Also, it is shown that if a linear operatör is an linear, then its continuous adjoint operator is an linear operator. And also, it is shown that if then .