BOOK REVIEW: "Palle Jorgensen and Feng Tian, Non-commutative Analysis." World Scientific 2017, xxviii+533 p., ISBN: 978-981-3202-11-5 (hardcover); 978-981-3202-12-2 (softcover); 978-981-3202-14-6 (ebook)

Abstract

As the authors mention in the Preface, the central themes of the book are: (i) Operators in Hilbert space; (ii) Multivariable spectral theory; (iii) Non-commutative analysis; (iv) Probability theory; (v) Unitary representations. The term "non-commutative analysis" is interpreted as including representations of non-Abelian groups, and non-Abelian algebras, with emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras).