Introduction to operator space theory /

The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Pisier, Gilles, 1950-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, U.K. ; New York : Cambridge University Press, 2003.
Colección:London Mathematical Society lecture note series ; 294.
Temas:
Operator spaces.
Espaces d'opérateurs.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Funktionalanalysis
Operatorraum
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Introduction to Operator Spaces
  • Completely bounded maps
  • Minimal tensor product
  • Minimal and maximal operator space structures on a Banach space
  • Projective tensor product
  • The Haagerup tensor product
  • Characterizations of operator algebras
  • The operator Hilbert space
  • Group C*-algebras
  • Examples and comments
  • Comparisons
  • Operator Spaces and C*-tensor products
  • C*-norms on tensor products
  • Nuclearity and approximation properties
  • C*
  • Kirchberg's theorem on decomposable maps
  • The weak expectation property
  • The local lifting property
  • Exactness
  • Local reflexivity
  • Grothendieck's theorem for operator spaces
  • Estimating the norms of sums of unitaries
  • Local theory of operator spaces
  • Completely isomorphic C*-algebras
  • Injective and projective operator spaces
  • Operator Spaces and Non Self-Adjoint Operator Algebras
  • Maximal tensor products and free products of non self-adjoint operator algebras
  • The Blechter-Paulsen factorization
  • Similarity problems
  • The Sz-nagy-halmos similarity problem
  • Solutions to the exercises.

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