On vectorial inner product spaces
Let be a real linear space. A vectorial inner product is a mapping from into a real ordered vector space with the properties of a usual inner product. Here we consider to be a -regular Yosida space, that is a Dedekind complete Yosida space such that , where is the set of all hypermaximal bands in . In Theorem 2.1.1 we assert that any -regular Yosida space is Riesz isomorphic to the space of all bounded real-valued mappings on a certain set . Next we prove Bessel Inequality and Parseval...