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Wegge-Olsen N.E. — K-Theory and C*-Algebras: a friendly approach
Wegge-Olsen N.E. — K-Theory and C*-Algebras: a friendly approach

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Название: K-Theory and C*-Algebras: a friendly approach

Автор: Wegge-Olsen N.E.


K-theory is often considered a complicated mathematical theory for specialists only. This book is an accessible introduction to the basics and provides detailed explanations of the various concepts required for a deeper understanding of the subject. Some familiarity with basic C*algebra theory is assumed. The book then follows a careful construction and analysis of the operator K-theory groups and proof of the results of K-theory, including Bott periodicity. Of specific interest to algebraists and geometrists, the book aims to give full instruction. No details are left out in the presentation and many instructive and generously hinted exercises are provided. Apart from K-theory, this book offers complete and self contained expositions of important advanced C*-algebraic constructions like tensor products, multiplier algebras and Hilbert modules.

Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 370

Добавлена в каталог: 24.11.2004

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Предметный указатель
$A^+$      2.1.6f
$A^\sim$      2.1.3
$K^0(X)$      13.3.2
$K^{-n}(X)$      13.3.4
$K_0(A)$      6.2 15.K
$K_1(A)$      7.1
$K_n(A)$      7.2.6
$K_\ast(A)$      8.B
$K_{00}(A)$      6.2 15.K
$\sigma$-additive functor      11.E
$\sigma$-unital $C^\ast$-algebra      1.2
$\tilda{K}^0(X)$      13.3.1
Additive functor      3C 11.1.1
Adjoined unit      1.2 2.1.3
Adjointable operator      15.2.1 15.E
AF-algebras      3.2.3 12.1
Algebraic direct limit      L.l
Algebraic tensor product of representations      T.5.1 T.5.3
Approximate unit      1.2
Approximation by projections      5.1.6
Atkinson’s theorem      14.1.1 17.1.6
Automorphisms of $\mathbb{K}$      1.10.2
Bases in tensor products      T.2.6
BDF-theory      3.G 3.H 3.1
Bott functor      11.1.1
Bott map      9.1.2 9.F 9.1
Bott periodicity      0.2.2 §9 9.J 11.2.1
Bott projection      5.1 7.G 8.F 9.J
Boundedness away from zero      15.G
Busby invariant      3.2.5 3.2.15
C*-equation      1.1
Calkin algebra      14.C
Carl Neumann criterion for invertibility      1.3
Cauchy — Schwarz inequality      15.1.3 15.C
Cech cohomology groups      13.H
Centralizer, double      2.2.6 2.E
Centralizer, double, left, right      2.2.7
Classical Fredholm index      §14
Close invertibles      4.2.1
Close invertibles, projections      5.2.6
Close invertibles, unitaries      4.2.4
Cofibre      6.4.6
Cofibre axiom      11.C
Compact adjointable operators      15.2.6
Compact operators      1.5
Compact perturbations      3.G §17
Compactification      2.1.2 2.B 2.C
Complementable Hilbert modules      15.3.1 15.3.9 15.1
Complementable Hilbert modules, ideals      15.J
Cone      6.4.5
Conjugate Hilbert space      T.P
Conjugate linear maps      T.4.1
Continuity of $K_0$      6.2.9
Continuity of $K_x$      7.1.7
Continuity of tensor maps      T.3.8 T.5.19 T.6.9 T.6.23
Continuous functors      11.E 11.1.1
Contractible $C^\ast$-algebra      6.4.1 6.4.4 6.4.7 6.H 11.1.3 16.8
Corona algebra      2.2.15 10.3
Countably generated Hilbert modules      15.4.7 15.P
Cross norm      T.3.2 T.6.21
Cuntz algebras      12.2
Cyclic projection      T.5.5f
Decomposition into positive and negative part      Appendix O
Deformation retraction      6.4.1
Dimension drop      7.D
Dimension group      12.1.1
Direct limit      Appendix L
Direct sum of Hilbert modules      15.1.8
Direct sum of Hilbert modules of $C^\ast$-algebras      2.1.4 2.D 3.2.3
Disorder in $C^\ast$-algebras      Appendix O
Double centralizer      2.2.6 2.E
Dual tensor norm      T.3.10f T.F
e-Theory      0.2.3
Elementary matrix operations      4.2.8 5.2.14
Elementary tensor      T.2.3
Enveloping $C^\ast$-algebra      T.L
Enveloping group      Appendix G
EQUIVALENCE      6.4.1 6.4.4
Equivalence of projections      5.2.1
Equivalence of projections of idempotents      5.B
Essential extension      3.2.1
Essential extension, ideal      1.4 2.1.1 2.2.14 15.2.10 T.K
Essential extension, spectrum      3.G
Essentially normal operators      3.G
Exact functor      11.1.1
Exact sequence      3.1.1
Exact sequence of $C^\ast$-algebra tensor products      T.6.26
Exact sequence of $C^\ast$-algebras      3.1.5
Exact sequence of AF-algebras      12.1.1
Exact sequence, long      8.2.1 11.1.4 11.1.12 13.3.4
Exact sequenceof K-groups      6.3.2 7.1.12
Exponential map      9.3.1 9.E
Extension of nuclear $C^\ast$-algebras      T.6.27
Extensions      3.2
Extensions, essential      3.2.1
Extensions, strong equivalence of      3.3.1
Extensions, strong isomorphism of      3.2.13
Extensions, sum of      3.3 3.3.5
Extensions, trivial      3.2.1 3.1
Extensions, weak isomorphism and weak equivalence of      3.E
Fibre of vector bundle      13.1.1
Finite $C^\ast$-algebras      5.F 6.1
Finite dimensional $C^\ast$-algebras      12.1.2 T.5.20
Finite rank operators      1.5
Finitely generated Hilbert modules      15.4
Fredholm alternative      14.A
Fredholm index      0.2.1 8.E §14 17.2
Fredholm matrices      17.2.2
Fredholm operators      14.1
Full Hilbert module      15.1.2
Functional calculus      1.3
Functorial K-theory      11.2.3
Generalized Atkinson’s theorem      17.1.6
Generalized Fredholm index      17.2
Generalized Fredholm operators      §17
GNS-construction      1.1 1.5 15.Q
Grothendieck group      Appendix G
Half exact functors      3.C 11.1
Half exactness of $K_0$      6.3.2
Half exactness of $K_1$      7.1.12
Halving projections      5.3.3ff 7.E 16.4f
Hilbert module      15.1.1 15.1.5
Hilbert module map      15.1.5
Hilbert module, full      15.1.2
Hilbert module, standard      15.1.7
Hilbert space over A      15.1.7
Hilbert — Schmidt operators      T.P
Homology functors      11.1
Homology theory      11.1.4
Homotopic, invertibles      4.2.1
Homotopic, morphims      6.4.1
Homotopic, projections      5.2.1 5.D
Homotopic, unitaries      4.2.4
Homotopy      4.2 9.2.9
Homotopy invariance of $K^0$      13.3.3
Homotopy invariance of $K_0$      6.4.3
Homotopy invariance of $K_1$      7.1.6
Homotopy invariant functors      11.1.1
Ideal      1.4 1.B
Ideal in tensor products      T.6.25 T.K
Ideal, essential      1.4 2.1.1 2.2.14 15.2.10 T.K
Idealizer      2.2.3
Idempotents      5B
Index map in K-theory      8.1.1
Induced vector bundle      13.2
Inductive limits      Appendix L 1.4 4.4 T.K
Infinite sums      1.7
Inner product in Hilbert modules      15.1.1
Inner product in Hilbert modules in tensor products      T.4 T.G
Irrational rotation algebra      12.3 12.G
Isometry      5.1.4 5.A
K-functors, surjectivity of      9.H
K-homology      0.2.3
K-idiomatic operations      0.2.2
K-masochist      7.2.3
Kasparov’s stabilization theorem      15.4.6
Kasparov’s technical theorem      2.2.15
KK-theory      0.2.3 3.3.9
Kuiper’s (generalized) theorem      16.8
Kunneth theorem      9.3.3
Laurent loop      9.2.1
Left multiplier      2.F 15.H
Lift of homotopies      4.4.2
Lift of invertibles      4.3.3
Lift of unitaries      4.3.5 17.1.2
Lifting map      3.1.2
Linear loops      9.2.1 9.2.6
Local $C^\ast$-algebras      5.B
Locally trivial vector bundle      13.1.4
Long Exact Sequence      8.2.1 11.1.4 11.1.12 13.3.4
Loops in $C^\ast$-algebras      7.2.2 9.2
Loops in topological groups      7.2.2
Loops, Polynomial, Laurent, Projection, Linear      9.2.1
Mapping cone      6.4.5 6.4.8 6.M 6.N 9.G
Mapping cylinder      6.M
Mapping torus      9.K
Matrix algebras      5.C 5.3.6 T.2.13
Maximal $C^\ast$-norm      T.6.6ff T.I
Mayer — Vietoris’ sequence      11.D
Mindex      17.2.1
Mobius strip      13.2.2
Morphisms      1.1
Multiplicative states      T.6.11
Multiplier algebras      2.2.2
Multiplier algebras, and tensor products      T.6.1 T.N
Multiplier algebras, K-theory for      10.2
Multipliers (left, right, quasi)      2.F
Murray von Neumann equivalence qf projections      5.2.2
Natural transformation      7.2.6 8.A
Neumann criterion for invertibility      1.3
Non-adjointable bounded operator      15.E
Non-commutative topology      1.11 2.A 2.B
Non-degenerate representation      2.2
Non-unital $C^\ast$-algebras      1.2
Norm in Hilbert modules      15.1.5
Normal elements      1.3
Normal Predholm operator      17.2.2
Normalized matrices      4.1.1
Nuclear $C^\ast$-algebras      T.6.18ff T.6.26f
Nuclear $C^\ast$-algebras, exact sequences of      T.2.26
Nuclearity of finite dimensional $C^\ast$-algebras      T.5.20
Nuclearity of finite dimensional $C^\ast$-algebras, of commutative $C^\ast$-algebras      T.6.20
Nuclearity of finite dimensional $C^\ast$-algebras, of inductive limits      T.M
Nuclearity of finite dimensional $C^\ast$-algebras, of multiplier algebras      T.N
Numerical radius      T.5.10
One point compactification      2.1.8
Operator algebras      1.5
Ordered group      6.1
Orthogonal complement      5.1.2 15.3.1
Orthogonal direct sum of $C^\ast$-algebras      2.1.4f 2.D 3.2.3
Orthogonal Hilbert modules      15.3.1
Partial isometry      5.1.4 5.A
Perforation in ordered groups      12.A
Polar decomposition      1.5 l.A 15.3.7f 15.L 17.1.5
Polarization identity      15.1.2
Polygonal homotopy      9.2.9
Portrait of $K_0$      6.2.7
Positive cone      6.1
Positive elements      Appendix O 15.2.5 1.6
Positive elements in abelian groups      6.1
Positive elements, spectrum of      1.3
Positive elements, strictly      15.4.5f
Positive functionals, tensor product of      T.B
Positive part of selfadjoint element      Appendix O
Powers — Rieffel projection      12.N
Pre-Hilbert module      15.1.1
Product state      T.5.7 T.5.11f
Projection loop      9.2.1 9.2.7
Projections      5.1.1
Projections in inductive limits      5.1.7 5.H
Projections, close      5.2.6
Projections, cyclic      T.5.5f
Projections, equivalence of      5.2
Projections, halving (or proper)      5.3.3ff 7.E 16.4f
Projections, skew      5.B 15.D
Projections, support/range      5.1.5
Projective modules      15.4.2 15.4.8
Projective plane      5.1
Proper map      2.A
Proper projection      see “Halving projection”
Pullback      3.2.6ff 3.D
Pure state      T.5.7f T.6.13
PV-sequence      9.3.3 9.K
Pythagoras’ equality      15.B
Quasi multiplier      2.F
Quotient norm      1.4
Quotient space (topological)      13.D
Reasonable tensor norm      T.3.12
Reduced K-group      13.3.1
Reduced suspension      13.3.4
Relative K-groups      13.G
Representation      1.5
Representation of Hilbert modules      15.Q
Representation, algebraic      T.5.1
Representation, non-degenerate      1.5 2.2
Representation, subcross      T.5.3f
Representation, universal      1.5
Representations, Algebraic tensor product of      T.5.1 T.5.3
Restriction of multiplicative state      T.6.11
Restriction of multiplicative state, of tensor maps      T.2.12 T.3.9 T.5.3 T.6.4 T.6.12f
Restriction of multiplicative state, of vector bundles      13.1.4
Riesz group      12.A
Right multiplier      2.F
Ring structure in $K_0$      6.L
RIP-group      12.A
Rotation algebra      12.3 12.Gff
Scale of $C^\ast$-algebra      6.1
Scaled ordered group      6.1
Section of vector bundles      13.4
Self dual Hilbert modules      15.1
Similar idempotents      5.B
Simplicity of $C^\ast$-algebra tensor products      T.6.25
Simplicity of $C^\ast$-algebra tensor products, of rotation algebras      12. J
Six term exact sequence      9.3.2
Skew projections      5.B 15.D
Spatial norm, formula for      T.5.14 T.5.16
Spatial tensor product      T.5
Spectral radius      1.3
Spectral theory      1.3
Spectrum      1.3
Spectrum, essential      3.G
Split exact functor      11.1.1
Split exact sequence      3.1.1
Split exact sequence of $C^\ast$-algebras      3.1.5
Split exactness of $K_0$ and $K_1$      8.2.2
Stability of $K_0$      6.2.10
Stability of $K_1$      7.1.9
Stabilization      0.2.2 1.10 17.2.2 17.3.2
Stabilization theorem      15.4.6
Stable functor      11.1.1
Stable multiplier algebras      10.3 16.6ff
Stably finite $C^\ast$-algebras      6.1
Standard exact sequence of $C^\ast$-algebras      3.1.5
Standard isomorphism      3.3.3
Standard unitary      7.G 9.1 9.J
State      T.5.7ff
State, product      T.5.7 T.5.11f
State, pure      T.5.7f
State, tracial      6.J
State, vector      T.5.7 T.5.10f
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