Completely Bounded Maps and Operator AlgebrasCambridge University Press, 2002 - 300 עמודים This book tours the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, along with some of their main applications. It requires only a basic background in functional analysis. The presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will appreciate how the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensible introduction to the theory of operator spaces. |
תוכן
Introduction | 1 |
Positive Maps | 9 |
Completely Positive Maps | 26 |
Dilation Theorems | 43 |
Commuting Contractions on Hilbert Space | 58 |
Completely Positive Maps into Mn | 73 |
Arvesons Extension Theorems | 84 |
Completely Bounded Maps | 97 |
Tensor Products and Joint Spectral Sets | 159 |
Abstract Characterizations of Operator Systems and Operator Spaces | 175 |
An Operator Space Bestiary | 186 |
Injective Envelopes | 206 |
Abstract Operator Algebras | 225 |
Completely Bounded Multilinear Maps and the Haagerup Tensor Norm | 239 |
Universal Operator Algebras and Factorization | 260 |
Similarity and Factorization | 273 |
Completely Bounded Homomorphisms | 120 |
Polynomially Bounded and PowerBounded Operators | 135 |
Applications to KSpectral Sets | 150 |
285 | |
297 | |
מהדורות אחרות - הצג הכל
Completely Bounded Maps and Operator Algebras <span dir=ltr>Vern Paulsen</span> תצוגה מקדימה מוגבלת - 2002 |
מונחים וביטויים נפוצים
A₁ Banach space bilinear bimodule bounded homomorphism bounded linear bounded operator C*-algebra with unit C*-subalgebra C₁ Chapter commuting contractions compact completely bounded maps completely contractive completely isometric isomorphism completely positive maps contractive homomorphism Corollary decomposition define denote dilation theorem E₁ example Exercise exists a Hilbert extension theorem factorization finite given h₁ Hausdorff space Hence Hilbert space homomorphism I(Sx identity map implies infimum injective envelope integers K-spectral K₁ Lemma linear functional linear map Math matrix norm MIN(V minimal n-tuple Neumann's inequality normed space Note operator algebra operator space structure operator system operator-valued Pisier polynomially bounded power-bounded proof of Theorem Proposition Prove result S₁ satisfying scalar self-adjoint sequence Show similar space H spectral set Stinespring representation subalgebra subspace supremum tensor product theory unital C*-algebra unital homomorphism unital operator algebra unitary dilation V₁ vector space Wittstock