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...
| Основен автор: | Pisier, Gilles, 1950- |
|---|---|
| Формат: | Електронна книга |
| Език: | English |
| Публикувано: |
Cambridge, U.K. ; New York :
Cambridge University Press,
2003.
|
| Серия: |
London Mathematical Society lecture note series ;
294. |
| Предмети: | |
| Онлайн достъп: |
http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=120691 |
| Подобни документи: |
Print version::
Introduction to operator space theory. |
Съдържание:
- 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.