Fundamentals of the Theory of Operator Algebras. V1: Elementary TheoryFundamentals of the Theory of Operator Algebras. V1 |
Contents
| xiii | |
| 1 | |
Chapter 2 Basics of Hilbert Space and Linear Operators | 75 |
Chapter 3 Banach Algebras | 173 |
Chapter 4 Elementary CAlgebra Theory | 236 |
Chapter 5 Elementary von Neumann Algebra Theory | 304 |
| 384 | |
| 387 | |
| 391 | |
Pure and Applied Mathematics | 399 |
Common terms and phrases
abelian von Neumann adjoint Banach algebra Banach space bounded linear functional bounded linear operator C*-algebra C*-algebra QI characteristic function clopen set closed subspace closure commutative compact Hausdorff space contains continuous function continuous linear functional converges Corollary corresponding countable defined denote dense elements of QI equation Exercise finite follows function calculus function f functions in C(X Hausdorff space Hence hermitian Hilbert space Hilbert–Schmidt homomorphism ideal in QI identity inner product inverse isomorphism Lemma linear space linear subspace mapping multiplicative linear functional Neumann algebra non-zero normal normed space null space operators acting orthogonal orthonormal basis polynomials projection Proof Proposition prove representation scalar self-adjoint element self-adjoint operator semi-norms sequence Show ſº sp(A spectral strong-operator topology subalgebra subset Suppose Theorem Tºx two-sided unit ball unitary operator vanishes vector space von Neumann algebra weak weak-operator