Stanisław 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.

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• Preface Introduction Preliminaries Part 1: Foundational Examples 1: Abelian von Neumann algebras 2: The Schatten-von Neumann classes Part 2: Tracial case 3: Noncommutative measure theory U+02014 tracial case 4: Weights and densities 5: Basic theory of decreasing rearrangements 6: 퐿 푝 and Orlicz spaces in the tracial case 7: Real interpolation and monotone spaces Part 3: General case 8: Basic elements of modular theory 9: Crossed products 10: Lp: 퐿 푝 and Orlicz spaces for general von Neumann algebras Part 4: Advanced Theory and Applications 11: Complex interpolation of noncommutative 퐿 푝 spaces 12: Extensions of maps to 퐿 푝 (M) spaces and applications 13: Haagerup's reduction theorem 14: Applications to quantum physics Bibliography Notation Index Subject Index

Stanisław 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.

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• Preface Introduction Preliminaries Part 1: Foundational Examples 1: Abelian von Neumann algebras 2: The Schatten-von Neumann classes Part 2: Tracial case 3: Noncommutative measure theory U+02014 tracial case 4: Weights and densities 5: Basic theory of decreasing rearrangements 6: 퐿 푝 and Orlicz spaces in the tracial case 7: Real interpolation and monotone spaces Part 3: General case 8: Basic elements of modular theory 9: Crossed products 10: Lp: 퐿 푝 and Orlicz spaces for general von Neumann algebras Part 4: Advanced Theory and Applications 11: Complex interpolation of noncommutative 퐿 푝 spaces 12: Extensions of maps to 퐿 푝 (M) spaces and applications 13: Haagerup's reduction theorem 14: Applications to quantum physics Bibliography Notation Index Subject Index

Stanisław 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.

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• Preface Introduction Preliminaries Part 1: Foundational Examples 1: Abelian von Neumann algebras 2: The Schatten-von Neumann classes Part 2: Tracial case 3: Noncommutative measure theory U+02014 tracial case 4: Weights and densities 5: Basic theory of decreasing rearrangements 6: 퐿 푝 and Orlicz spaces in the tracial case 7: Real interpolation and monotone spaces Part 3: General case 8: Basic elements of modular theory 9: Crossed products 10: Lp: 퐿 푝 and Orlicz spaces for general von Neumann algebras Part 4: Advanced Theory and Applications 11: Complex interpolation of noncommutative 퐿 푝 spaces 12: Extensions of maps to 퐿 푝 (M) spaces and applications 13: Haagerup's reduction theorem 14: Applications to quantum physics Bibliography Notation Index Subject Index