Ceauşu, Traian Elements of the theory of noncommutative integration. (Elemente de teoria integrării necomutative). (Romanian) Zbl 0592.46057 Monografii Matematice, 25. Timișora: Universitatea din Timișoara, Facultatea de Științe ale Naturii, Secția Matematică. V, 169 p. Lei 15.00 (1985). 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 Keywords:structure of commutative von Neumann algebras; H-algebras; Stone spaces; dimension function; measurable operators; convergence problems; integrable operators; harmonic analysis; noncommutative case PDFBibTeX XML