INTEGRATION ON JORDAN ALGEBRAS

In this paper the author gives a nonassociative generalization of abstract integration on JBW-algebras - Jordan Banach algebras having a predual space. Using a faithful normal finite trace on a JBW-algebra , a topology of convergence in measure is introduced and the Jordan algebra of all measurable elements with respect to is constructed as the completion of in this topology. The spaces and are introduced for and it is shown that they can be considered as the spaces of all integrable and square-integrable elements, respectively, of . As in the case of von Neumann algebras it is proved that is isometrically isomorphic to the Banach space predual to .Bibliography: 32 titles.

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