همریختی ها و مشتقات

we have devided the thesis in to five chapters. the first recollects facts from purely algebraic theory of jordan algebras and also basic properties of jb and jb* - algebras which are needed in the sequel. in the second chapter we extend to jb* - algebras, a classical result due to cleveland [8]. this result shows shows the weakness of jb* - norm topology on a jb* - algebera. in chapter three, we have a short look at the representation theory of jordan algebras and the concept of a module for jordan algebras. we define banach jordan modules for banach jordan algebras and we prove some results related to different annihilating sests of submodules. some of theses results are needed in chapter four. in chapter four, we consider the problem of continuity of module valued derivations from jb* - algebras in to banach jordan modules. we show that the ringrose sresult [27], which shows that any module derivation of a c* - algebra is continuous, is not valid for jb* - algebras. we prove the continuity of module valued derivations of jb* - algebras in certain cases, however, we show the existance of discontinuous module valued derivations in some other cases. this result also proves the invalidity of another theorm due to sinclair [35], for jb* - algebras. chapter five is mainly a collection of open problems and some partial results related to them.