Modular Theory in Operator Algebras

Author: Serban Valentin Stratila, Institute of Mathematics of the Romanian Academy, Romania

The text provides detailed discussion of normal weights, conditional expectations and U. Haagerup’s operator-valued weights, groups of automorphisms and their spectral theory, dual theory for noncommutative groups, and crossed products of von Neumann algebras by actions of groups and dual of groups, which enable the extension of M. Takesaki duality for noncommutative groups of automorphisms. It also contains detailed discussion on the group measure space construction of factors and information about ITPFI factors and Krieger factors. The core of the book is the continuous decomposition of A. Connes and M. Takesaki and discrete decomposition of A. Connes for type III factors. It also explores new results, such as the A. Ocneanu’s result on the actions of amenable groups on the hyperfinite factor, H. Kosaki’s extension of the V. Jones index to arbitrary factors and F. Radulescu’s examples of non-hyperfinite factors.

ISBN 978-110-489-60-7 | First published in 2021 Co-publisher: Cambridge University Press