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Elements of the theory of noncommutative integration. (Elemente de teoria integrării necomutative). (Romanian) Zbl 0592.46057

The present monograph contains the lectures given by the author in ”Linear Operators and Harmonic Analysis Seminar” from University of Timişoara.
The work has three sections. In the first part, the structure of commutative von Neumann algebras, H-algebras, Stone spaces and dimension function are presented. The second one is dedicated to the study of measurable operators. The convergence problems are analysed. The last section contains a survey on integrable operators.
This study is useful to those who are interested in an extension of results from commutative harmonic analysis to the noncommutative case. Applications of the study in theoretical physics, quantum mechanics, and other branches are presented.
Reviewer: I.Valuşescu

MSC:

46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis