Operator Space Tensor Norms

Javier Alejandro Chávez-Domínguez is an Associate Professor in the Department of Mathematics of the University of Oklahoma (USA). His main research interest is Functional Analysis with an emphasis on its non-linear and non-commutative aspects, particularly Operator Spaces, Tensor Products and Operator Ideals, and Quantum Graphs/Metric Spaces.  Verónica Dimant is a Full Professor at the University of San Andrés (Argentina) and Independent Researcher at CONICET. Her research interest lies in Non-linear Functional Analysis with a focus on Holomorphy, Polynomials and Tensor Products in Banach spaces and operator spaces.  Daniel Galicer is an Associate Professor at Universidad Torcuato Di Tella (Argentina) and an Independent Researcher at IMAS-CONICET. His research focuses on Functional Analysis, with an emphasis on the Local Theory of Banach Spaces, Infinite-Dimensional Analysis, Asymptotic Geometric Analysis, Tensor Products, and the interactions between Analysis and Probability.

• Chapter 1. Preliminaries.- Chapter 2. Introduction to operator space tensor norms.- Chapter 3. Finite and cofinite hulls.- Chapter 4. The five basic lemmas.- Chapter 5. Dual operator space tensor norms.- Chapter 6. The completely bounded approximation property.- Chapter 7. Mapping ideals.- Chapter 8. Maximal operator space mapping ideals.- Chapter 9. Minimal operator space mapping ideals.- Chapter 10. Completely projective/injective tensor norms.- Chapter 11. Injective/projective hulls and accessibility.- Chapter 12. Natural operator space tensor norms.- Chapter 13. Conclusions and some open questions.