Theory of Operator Algebras ISpringer Science & Business Media, 20 nov. 2001 - 415 pages Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects. |
Table des matières
II | 1 |
III | 2 |
IV | 6 |
V | 13 |
VI | 17 |
VII | 21 |
VIII | 23 |
IX | 25 |
XXIX | 179 |
XXX | 181 |
XXXI | 182 |
XXXII | 188 |
XXXIII | 192 |
XXXIV | 203 |
XXXV | 220 |
XXXVI | 229 |
X | 31 |
XI | 35 |
XII | 47 |
XIII | 50 |
XIV | 54 |
XV | 55 |
XVI | 58 |
XVII | 59 |
XVIII | 67 |
XIX | 71 |
XX | 79 |
XXI | 99 |
XXII | 101 |
XXIII | 102 |
XXIV | 120 |
XXV | 130 |
XXVI | 139 |
XXVII | 147 |
XXVIII | 157 |
XXXVII | 230 |
XXXVIII | 253 |
XXXIX | 264 |
XL | 289 |
XLI | 290 |
XLII | 309 |
XLIII | 335 |
XLIV | 336 |
XLV | 344 |
XLVI | 352 |
XLVII | 359 |
XLVIII | 362 |
XLIX | 374 |
L | 375 |
387 | |
389 | |
409 | |
411 | |
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Expressions et termes fréquents
A₁ A₂ abelian abelian von Neumann Banach algebra Banach space Borel set Borel space bounded C*-algebra central projection closure commutes completely positive conjugate space continuous function converges strongly convex countable cross-norm cyclic representation define denote dense dµ(v dµ(w e₁ E₂ element enveloping von Neumann equivalent exists f₁ faithful semifinite normal follows Hence Hilbert space homomorphism invariant isometry isomorphism LC(H lower semicontinuous M₁ M₂ maximal abelian measure minimal projection N₁ Neumann algebra norm o-finite o-strong o-strongly operator algebras orthogonal polar decomposition Polish space positive linear functional predual PROOF Q.E.D. Corollary Q.E.D. Definition Q.E.D. Lemma Q.E.D. Proposition Q.E.D. Theorem resp self-adjoint semifinite normal trace sequence Show space H subalgebra Suppose tensor product topology unique unit ball unitary vector von Neumann algebra w₁ x₁