It is shown that the matrix normed structure of a non-unital operator algebra determines that of its unitization. This makes the study of certain unital operator algebras much easier and provides several interesting

We describe the alternative elements in An = R n the CayleyDickson algebras for n ≥ 4. Also we “measure” the failure of An with n ≥ 4 of being a normed algebra in terms of the alternative elements.

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to define Clifford algebras with scalars in arbitrary rings and provides new suggestions for an infinite-dimensional approach. Furthermore, I give a quick review...