Theory of Operator Spaces

ISBN-13: 9781470465056 / Miękka / 2022 / 358 str.

Zhong-Jin Ruan

Spis treści

• Matrix and operator conventions
• Examples and three basic theorems: The representation theorem
• Constructions and examples
• The extension theorem
• Operator systems and decompositions
• Injectivity
• Tensor products: The projective tensor product
• The injective tensor product
• The Haagerup tensor product
• Infinite matrices and asymptotic constructions
• The Grothendieck programme: The approximation property
• Mapping spaces
• Absolutely summing mappings
• Local theory and integrality: Local reflexivity, exactness, and nuclearity
• Local reflexivity and exact integrality
• Some algebraic applications: Non-commutative harmonic analysis
• An abstract characterization for non-self-adjoint operator algebras
• Preliminaries
• Bibliography
• Index of notation
• Index