Generalization of Maeda's theorem (Q1822312)

The theorem of S. Maeda concerning the characterization of finite measures on a quantum logic of all closed subspaces of a Hilbert space of dimension \(\neq 2\) is generalized to the case of \(\sigma\)-finite measures with possible infinite values showing that the following assertions are equivalent: (i) there is unique positive bilinear form \(t\) with a dense domain such that \(m(M)=tr t\circ P^ M\) if \(t\circ P^ M\in Tr(H)\) and \(m(M)=\infty\) otherwise; (ii) \(m\) is totally additive; (iii) \(m\) has a support.