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On vectorial inner product spaces

João de Deus Marques (2000)

Czechoslovak Mathematical Journal

Let E be a real linear space. A vectorial inner product is a mapping from E × E into a real ordered vector space Y with the properties of a usual inner product. Here we consider Y to be a -regular Yosida space, that is a Dedekind complete Yosida space such that J J = { 0 } , where is the set of all hypermaximal bands in Y . In Theorem 2.1.1 we assert that any -regular Yosida space is Riesz isomorphic to the space B ( A ) of all bounded real-valued mappings on a certain set A . Next we prove Bessel Inequality and Parseval...

Ortogonalidad en espacios normados generalizados.

Rosa Fernández (1988)

Stochastica

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.

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