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Introduction to operator space theory

Author: Gilles Pisier
Publisher: Cambridge, U.K. ; New York : Cambridge University Press, 2003.
Series: London Mathematical Society lecture note series, 294.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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 emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*-algebras,  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Gilles Pisier
ISBN: 0521811651 9780521811651
OCLC Number: 50582823
Description: vii, 478 pages ; 23 cm.
Contents: 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.
Series Title: London Mathematical Society lecture note series, 294.
Responsibility: Gilles Pisier.
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Abstract:

An introduction to the theory of operator spaces, emphasising applications to C*-algebras.  Read more...

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'The tone of the book is quite informal, friendly and inviting. Even to experts in the field, a large proportion of the results, and certainly of the proofs, will be new and stimulating. ... there Read more...

 
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