ON BOUNDEDNESS AND CONTNUITY OF JORDAN, ORDINARY AND QUADRATIC PRODUCT IN ALTERNATIVE SEMI-PRIME ALGEBRAS

Abstract

In this work we prove that, if A is an alternative semi-prime algebra, which is considered as a complete convex bornological vector space (respectively, completely bornological locally convex space) and its bornology has a net, then there is equivalent between separating boundedness (resp. separating continuity) of Jordan, ordinary product and quadratic product. If A is again topological, then the boundedness is global and if A is Fr´echet space, there is an equivalence between the continuity of these three products.