Weights on Jordan Banach algebras
The main result of the paper is the following Jordanized version of the \textit{U. Haagerup} theorem [J. Funct. Anal. 19, 302-317 (1975; Zbl 0304.46043)] Theorem. Let \(\phi\) be a weight on a JBW-algebra A. The following conditions are equivalent: (1) \(\phi\) is completely additive; (2) \(\phi\) is normal; (3) \(\phi\) is weakly lower semicontinuous; (4) \(\phi (a)=\sup \{\psi (a)\), \(\psi\in F\}\forall a\in A^+\), where F is a family of positive normal functionals; (5) \(\phi (a)=\sum \psi_ i(a)\forall a\in A^+\), where \(\{\psi_ i\}\) is a family of positive normal functionals.
Jordanized version of the Haagerup theorem
scientific article; zbMATH DE number 4028174