Contents

• Contents
• Short History
• Operator Spaces and Completely Bounded Maps
  • Basic facts
  • Ruan's theorem
  • Elementary constructions
  • The space $\mathit{CB}(X,Y)$
  • The dual
  • Direct sums
  • $\mathit{MIN}$ and $\mathit{MAX}$
  • Injective operator spaces
• Operator Systems and Completely Positive Maps
  • Definitions
  • Characterization
  • Matrix order unit norm
  • Injective operator systems
• Hilbertian Operator Spaces
  • The spaces
  • The morphisms
  • The column Hilbert space ${\mathcal{C}}_\H$
  • Column Hilbert space factorization
• Multiplicative Structures
  • Operator modules
  • Completely bounded module homomorphisms
  • Operator algebras
• Tensor Products
  • Operator space tensor products
  • Injective operator space tensor product
  • Projective operator space tensor product
  • The Haagerup tensor product
  • Completely bounded bilinear mappings
  • Module tensor products
• Complete Local Reflexivity
• Completely Bounded Multilinear Mappings
• Automatic Complete Boundedness
• Convexity
  • Matrix convexity
  • Matrix extreme points
  • $C^*$-convexity
  • $C^*$-extreme points
• Mapping Spaces
  • Completely nuclear mappings
  • Completely integral mappings
• Appendix
  • Tensor products
  • Interpolation
• Symbols
  • Sets
  • Banach spaces
  • Algebras
  • Ideals
  • Mapping spaces
  • Operator spaces
  • Special operator spaces
  • Norms
  • Matrices
  • Tensor products
  • Tensor norms
  • Operator modules
  • Mappings
  • Isomorphisms
  • Miscellanea
• Bibliography
• Index
• About this document ...