 -spectrum 130
A-module 141
Abelian C*-algebra 26 65
Action of group 11
Additive 1-cocycle 152
AF algebra 25
Affiliated 147
Algebra of G-finite elements 46
Analytic element 17
Analytic elements for perturbed groups 126
Antisymmetric bicharacter 188
Approximate identity 103
Approximately finite dimensional 25
Approximately inner derivation 36
Automatic continuity of derivations 48
Automorphism 4
Borchers spectrum 130
Bounded derivation 5
Bounded perturbations 123
CAR algebra 173 234
Central sequence 7
Class of smooth elements 39
Closable operator 9
Closed operator 9
Closed under C*-functional analysis 21
Closure of operator 10
Coboundary 152
Cocycle 123
Cohomology 37
Commuting with group action 113
Complete dissipation 4 241
Completely positive map 245
Condition r 153 198
Connes spectrum 130
Conservative derivation 29 53
Contraction 13
Convolution semigroup of measures 256
Core problem 26
Crossed product 11
Cuntz algebra 237
Derivation 4
Derivation theorem 115
Differentiable element 39
Dimension of locally compact space 26
Direct sum 7
Dispersive operator 54
Dissipation 4 241
Dissipative operator 12
Domain of derivation 4
Dual basis for Lie algebra 193
Eigenunitaries 188
Ergodic action 185 226
Essential hereditary subalgebra 59
Finite range interaction 9
Fixed point algebra 44
Flow 32 66
Formal hamiltonian 8
Fourier transform 41
Frechet topology 49
Free action 79 225
Free flow 9
Frequency of point 81
Functional analysis of domain 21
G-covariant representation 137
G-finite elements for abelian actions 46
G-finite elements for compact actions 47
G-flow 66
G-prime 130
G-simple 130
Generalized Schwarz’s inequality 5
Generator 5 16
Generator of flow 66
Graph 2 0
| Group algebra 41
Hereditary subalgebra 59 129
Infinitely differentiable element 39
Infinitesmal generator 5
Inner derivation 5
Interaction 8
Invariant derivation 99 165
Invariant dissipative operator 102
Ising model 8
Lattice 7
Left multiplier 140
Lipschitz continuous 86
Local kernel property 33
Local operator 78
Locality 38
Locally free action 79
Locally free flow 79
Maximal partial isometry 148
Module map 141
Multiplier algebra 5
n times differentiable element 39
n-positive map 245
Negative definite function 256
Noncomir.utative vectorfield 34 184
Noncommutative manifold 35
Norm continuous group 5
One-parameter group 4
Orbit segment 33
Outer derivation 5
Partial cocycle 143
Period of point 81
Polynomially bounded 89
Pre-closed operator 9
Pre-generator 9 16
Quantum spin system 7
Quasi conservative derivation 29
Quasifree action 235
Restricted direct sum 7
Restriction set 32
Schwarz’s inequality 14
Self-determining set 32
Skew symmetric operator 24
Smooth element 39
Smoothness of 1-cocycles 124
Spectral subspaces for abelian actions 42
Spectral subspaces for compact actions 46
Spectral theory for group actions 41
Spectrum of abelian C*-algebra 27 65
Spectrum of group action 42
Stabilizer group 74
State 14
Strong topological transitivity 227
Strongly continuous group 4
Strongly continuous semi-group 5
Strongly n-positive map 245
Summable sequence 7
Tangent functional 12
Topological transitivity 227
Totally disconnected 27
Translationally invariant 9
Trivial central sequence 7
Twisted derivation 116
Twisted negative definite function 251
UHF-algebra 8
Unbounded derivation 7
Uniform radius of analyticity 195
Uniformly hyperfinite algebra 8
Uniformly locally free action 79
Uniformly locally free flow 79
Uniquely ergodic 158
Vector field 34
Velocity of flow 86
Well-behaved element 29
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