Introduction to the theory of noncommutative integration
The paper is a review of the progress in the theory of noncommutative integration since the well known Segal's work with the emphasis on the works of A. N. Sherstnev and his disciples in Kazan. It contains sections: 1. Integration in von Neumann algebras. 2. On the integration in JBW-algebras. 3. On a problem of integration with respect to unbounded measures on the projections. In the first section various ways to generalize the Segal's theory are described, among them the description of the space \(L_ 1\) with respect to a weight in terms of integrable bilinear forms and constructions of scales of \(L_ p\)-spaces proposed by Sherstnev, Trunov, Haagerup and many others. The second section deals with similar questions in the JBW-setting and is based mainly on Trunov's work. In the third section results of Sherstnev and Lugovaya are formulated.
integration with respect to unbounded measures on the projections
scientific article; zbMATH DE number 3998539
scientific article