Banach F-modüllerinin merkezi ve F-ortomorfizmalar üzerinde genişletilmiş sonuçlar

(Huijsmans and Pagter [12]) proved that when A is an unital Archimedean f-algebra, the equality A'' = (A' )n' holds, where (A')n' is the collection of all order continuous linear functionals on A' . Our study bases on this conclusion. If E is a Banach lattice, C(K) is the Banach algebra of continuous functions on K with the sup norm where K is a compact Hausdorff space and L(E) is the bounded linear operators on E , then a mapping m:C(K)?L(E) is a bounded unital algebra homomorphism. Some claims concerning on the center of E with this idea was shown in (Orhon [17]). In this work, taking A as an unital Archimedean f-algebra instead of C(K) , we generalized some of the results of (Orhon [17]). Here, it was assumed that A is an Archimedean f-algebra with unit element and L , M are two f-modules over A . Then it was shown that L'' , the second order dual of L , is an f-module over A'' where A'' is the second order dual of A . Moreover the concept of topologically fullness over A'' was defined and proved that A'' is a topologically full over A'' . In addition, in this work it was assumed that an operator T is an f-orthomorphism from L to M over A'' and it was shown that T'' is an f-orthomorphism, where T'' is the second adjoint of T from L'' to M'' . These conclusions obtained from here generalize some of the results of (Turan [14]). Keywords: Banach Lattice, Center, F-Algebra, F-Module, Dedekind Complete