In fact, if X is any vector space on which the primitive Banach algebra A acts faithfully and irreducibly, then X can be converted in a Banach space in such a way that the requirements in Theorem 0 are satisfied and even the inclusion A9BL(X ) is contractive. Roughly speaking, the aim of this paper is to prove the appropriate Jordan variant of Theorem 0. The notion of primitiveness for Jordan a...

In this article, the separability of real normed spaces and its properties are mainly formalized. In the first section, it is proved that a real normed subspace is separable if it is generated by a countable subset. We used here the fact that the rational numbers form a dense subset of the real numbers. In the second section, the basic properties of the separable normed spaces are discussed. It...

The octonionic X-product gives to the octonions a flexibility not found in the other real division algebras (reals, complexes, quaternions). The pattern of this flexibility is investigated here. supported by a grant from ..., well, no one, really. 0