C*-Algebras and Operator TheoryThis book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required. |
Contents
| 1 | |
Chapter 2 CAlgebras and Hilbert Space Operators | 35 |
Chapter 3 Ideals and Positive Functionals | 77 |
Chapter 4 Von Neumann Algebras | 112 |
Chapter 5 Representations of CAlgebras | 140 |
Chapter 6 Direct Limits and Tensor Products | 173 |
Chapter 7 KTheory of CAlgebras | 217 |
Appendix | 267 |
Notes | 277 |
References | 279 |
| 281 | |
| 283 | |
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Common terms and phrases
AF-algebra approximate unit Banach algebra Banach space C*-algebra C*-norm canonical map closed ideal closed unit ball closed vector subspace Co(N commutes compact Hausdorff space compact operator contains converges Corollary define denote dense diagram direct limit Example exists finite finite-dimensional follows from Theorem Fredholm Gelfand representation Hausdorff space Hence hereditary C*-subalgebra hermitian Hilbert space homomorphism inclusion ind(u injective integer invertible isometric isomorphism ker(u Ko(A Ko(B Lš(H left ideal Lemma Let H linear map linear span Neumann algebra non-empty norm orthonormal basis positive linear functional postliminal Prim(A Proof PS(A Remark representation H self-adjoint sequence of C*-algebras sesquilinear form short exact sequence space H strongly subalgebra subset suppose surjective topology tracial unilateral shift unique unit vector unital Banach algebra unital C*-algebra unital homomorphism unitarily equivalent unitary vector space von Neumann algebra weak zero