Noncommutative measures and Lp and Orlicz Spaces, with Applications to Quantum Physics

Stanislaw Goldstein, Professor, Head of Department of Applied Computer Science, University of Lodz, Faculty of Mathematics and Computer Science,Louis Labuschagne, Director: Focus Area for Pure and Applied Analytics, North-West University, PVT, School of Mathematics & Statistical Science

Stanislaw Goldstein began working at the University of Lodz in 1977 and continues there till this day, holding a chair at the Faculty of Mathematics and Computer Science. He earned his PhD in 1978 and became a full professor in 2001. In 1989-1990 he spent a year in Bielefeld-Bochum-Stochastik, King's College London and Nottingham University as a Humboldt Fellow. His research interests are primarily operator algebras and noncommutative measure theory.

Louis Labuschagne obtained his PhD in 1988 in the field of Single Linear Operator theory. He started his professional academic career in the same year at Stellenbosch University, moving to the University of Pretoria in 1992. This move also coincided with a shift in his research focus to Operator Algebras and their application to Quantum Theory. After spending 19 years in Pretoria, first at the University of Pretoria and then UNISA from 2001, he took up an appointment at North-West University in January 2011, where he currently serves as director of the Focus Area for Pure and Applied Analytics.

PrefaceIntroductionPreliminariesPart 1: Foundational Examples1. Abelian von Neumann algebras2. The Schatten-von Neumann classesPart 2: Tracial case3. Noncommutative measure theory U+02014 tracial case4. Weights and densities5. Basic theory of decreasing rearrangements6. ??sup??/sup and Orlicz spaces in the tracial case7. Real interpolation and monotone spacesPart 3: General case8. Basic elements of modular theory9. Crossed products10. L^p: ??sup??/sup and Orlicz spaces for general von Neumann algebrasPart 4: Advanced Theory and Applications11. Complex interpolation of noncommutative ??sup??/sup spaces12. Extensions of maps to ??sup??/sup(M) spaces and applications13. Haagerup's reduction theorem14. Applications to quantum physicsBibliographyNotation IndexSubject Index