Riesz cebirsel değerli Banach-Stone teoremleri

Let X, Y be compact Hausdorff spaces and let E, F be both Banach lattices and Riesz algebras. The main result of this thesis is following: If F has no zero-divisor and there exists a Riesz algebraic isomorphism T: C(X,E) to C(Y,F) such that Tf has no zero if f has none, then X is homeomorphic to Y and E is Riesz algebraically isomorphic to F. This result is taken from the paper of Banach-Stone theorems and Riesz algebras.This thesis consists of four chapters. In chapter 1, it is given some necessary definitions in topology, which is used in other chapters. In section 2, we present Riesz spaces, Riesz homomorphisms on C(X) spaces and Riesz algebras which given some properties. In section 3 is devoted to the proofs of the versions of the Banach-Stone theorem. Finally, in section 4, it is proved that under some certain conditions X and Y are homeomorphic, E and F are Riesz algebraically isomorphic when C(X,E) and C(Y,F) are Riesz algebraically isomorphic.