On a completion of prehilbertian spaces.
On an -Birkhoff orthogonality.
On isomorphisms by orthogonality of a normed space and an inner product space.
On representations of partial *-algebras based on -weights.
On the semi-inner product in locally convex spaces.
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...
Orthogonal constant mappings in isosceles orthogonal spaces
Ortogonalidad en espacios normados generalizados.
Some generalized notions of James' orthogonality and orthogonality in the Pythagorean sense are defined and studied in the case of generalized normed spaces derived from generalized inner products.