Orthonormalbasen in der nichtarchimedischen Funktionentheorie

In this paper one finds a new method to calculate problems concerning affinoid algebras. The method which uses orthonormal bases in normed vector spaces is developed in the first two paragraphs and is applied to affinoid algebras later on. In a simple way there are obtained nearly all results about affinoid algebras which are already known. Further this method gives new information about the functor F which associates to each affinoid space X an affine algebraic variety . In detail: F is compatible with extensions of the field k (if affinoid spaces are considered, k algebraically closed, n arbitrary) and F is compatible with the cartesian product. These problems are treated in the language of affinoid algebras.