Advanced Search

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