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Arveson W. — An Invitation to C-Algebras
Arveson W. — An Invitation to C-Algebras

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Название: An Invitation to C-Algebras

Автор: Arveson W.


This book is an introduction to $C^*$-algebras and their representations on Hilbert spaces. The presentation is as simple and concrete as possible; the book is written for a second-year graduate student who is familiar with the basic results of functional analysis, measure theory and Hilbert spaces. The author does not aim for great generality, but confines himself to the best-known and also to the most important parts of the theory and the applications. Because of the manner in which it is written, the book should be of special interest to physicists for whom it opens an important area of modern mathematics. In particular, chapter 1 can be used as a bare-bones introduction to $C^*$-algebras where sections 2.1 and 2.3 contain the basic structure theory for Type 1 von Neumann algebras.

Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1976

Количество страниц: 106

Добавлена в каталог: 09.04.2005

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Предметный указатель
$G_\delta$      62
$\mu$-measurable      77
*-isomorphism      2
Abelian projection      56
Absolutely measurable      77
Algebraically equivalent operators      2
Analytic Borel space      71
Analytic set      64
Approximate identity, approximate unit      36
Axiom of Choice      75 79
Borel function      69
Borel isomorphism      69
Borel set      64
Borel space      69
Borel transversal      77
C*-algebra      2
C*-algebra of operators      1
CCR algebra      23
Central cover      44
Central subrepresentation      44
Commutant      5
Compact operator      17
Composition series of a C*-algebra      25
Countably generated Borel space      72
Countably separated Borel space      69
Cross section for a function      74
Decomposable operator algebra      89
Diagonal operator      89
Direct product of C*-algebras      21
Direct sum of C*-algebras      21
Disjoint representations      43
Double commutant theorem      5
Elementary C*-algebra      21
Equivalent measures      51
Equivalent representations      14
Equivalent sets of representations      49
Ergodic equivalence relation      78
Factor      56
Functional calculus      4
GCR algebra      24
GCR operator      26
Gelfand — Naimark theorem      34
GNS construction      28
Homogeneous von Neumann algebra      58
Ideal      10
Involution      2
Irreducible representation      14
Kaplansky’s density theorem      7
localization      56
Measure class      53
Minimal projection      17
Multiple of a representation      20
Multiplicity function      21 50 55 100
Multiplicity-free representation      41
Nondegenerate representation      14
Normal operator      3 4
Null space of a set of operators      5
Open sieve      62
Oribt space      76
Orthogonal subrepresentations      41
Partition of a space      66
Polar decomposition      6
Polish space      61
Positive element      35
Positive linear functional      27
Primitive ideal      82
Pure state      29
Quotient of a Borel space      70
Quotient of a C*-algebra      11
Refinement of a partition      66
Representation      13
Saturated Borel set      70
Schwarz inequality for states      28
Self-adjoint set of operators      5
Separable C*-algebra      8
Separated sets      65
Sieve      62
Singular measures      51
Spectrum of a C*-algebra      2 83
Standard Borel space      69
State      27
Structure space      82
Subrepresentation      19
Subspace of a Borel space      69
Transversal for an equivalence relation      45
Trivial ergodic measure      78
Type I C*-algebra      59
Type I representation      47
Type I von Neumann algebra      57
von Neumann algebra      6
Well-ordered Polish space      75
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