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| Douglas R.G. — Banach algebra techniques in operator theory |
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| Предметный указатель |
*-homomorphism 88 110
Absolute continuity, of measures 104
Absolutely convergent Fourier series 56 61
Abstract index 36 62 133 138
Abstract index group 36 38
Adjoint of bounded linear transformation 30
Adjoint of closed, densely defined linear transformation 119
Adjoint of Hilbert space operator 81—82
Alaoglu theorem 10
Algebra of bounded holomorphic functions 26 150
Annihilator, of subspace 30 80
Asymptotically multiplicative functions 169
Atkinson theorem 128
Automorphism of Banach algebra 61
Automorphism of C*-algebra, inner 143
Automorphism of C*-algebra, weak 144
Banach algebra 34 32—62
Banach space 2 1—31
Banach theorem 13 31
Beurling theorem 45 153
Bilateral shift 89
Boundary, for function algebra 61
Bounded below, operator 83
Bounded variation, function 14
Brown — Halmos theorem 182
C*-algebra 91
Calkin algebra 127
Cauchy — Schwarz inequality 64
Cech cohomology group 38
Center, of algebra 196
Characteristic function 18
Circle group 51
Classical index 130 138
Closed convex hull 182
Closed graph theorem 29
Cobum theorem 184 185 205
Cohomotopy group 39
Commutant, of algebra 108
Commutator 180
Commutator, ideal 145 179
Compact operator 121 145
Complete metric space 2
Conjugate space 6
Convolution product 54
Corona theorem 156 173
Cross-section map 178
Cyclic vector 105 157
Dimension, Hilbert space 76 79
Direct sum of Banach spaces 29
Direct sum of Hilbert spaces 78
Directed set 3
Dirichlet problem 171
Disk algebra 51—53
Division algebra 42
Eigenspace, generalized 131
Essential range 57
Essential resolvent 191
Essential spectrum 190 191
Essentially bounded 24
Exponential map 36
Extensions, of C*-algebras 205
Extreme point 28 78
Fatou theorem 174
Fiber, of  172
Finite rank operator 59 121
Fourier coefficient 55
Fourier series 55
Fredholm alternative 131
Fredholm integral operator 125
Fredholm operator 127
Fuglede theorem 114 120
Function algebra 51
Functional calculus 93 99
Functional calculus, extended 112—114
Gelfand theorem 44 45
Gelfand transform 40
Gelfand — Mazur theorem 42
Gelfand — Naimark theorem 93
Gleason — Whitney theorem 164
Gohberg theorem 146
Gohberg — Krupnik theorem 207
Gram — Schmidt orthogonalization process 79
Grothendieck theorem 30
Hahn — Banach theorem 11 12 78
Hankel matrix 203
Hankel operator 203
Hardy space 26 70 149—176
Harmonic extension 168
Hartman theorem 183 204
Hartman — Wintner theorem 179 183
Hausdorff-Toeplitz theorem 115
Hellinger — Toeplitz theorem 116
Helson — Szego theorem 187
Hermitian operator 84
Hilbert space 63—80 66
Idempotent operator 116—117
Indicator function see Characteristic function
Initial space, of partial isometry 95
Inner function 152
Inner product 63
Inner product space 64
Inner-outer factorization 158
Integral operator 125 132 145
Invariant subspace 98
Invariant subspace, simply 151—152
Involution, of Banach algebras 82 91
Irreducible subset 141
Isometry 95 117 146
Isomorphism, of Hilbert spaces 76
Jensen's inequality 174
Kernel of integral operator 126
Kernel of operator 83
Kolmogrov — Krein theorem 175
Krein theorem 147
Krein — Mil'man theorem 28
Krein — Smul'yan theorem 30
Lebesgue space 7 23—26 68—70
Linear functional 5 72
Linear transformation, bounded 21
Linear transformation, closable 118
Linear transformation, closure of 118
| Linear transformation, self-adjoint 119
Linear transformation, symmetric 119
Localization, of C*-algebras 196
Matrix operator entries 116--117
Maximal abelian subalgebra 88
Maximal ideal space 44
Metric 2
Metric space 2
Multiplication operator 87
Multiplicative linear functional 32 39
Nehari theorem 203
Net 3
Net, Cauchy 3
Newman theorem 173
Norm 1
Norm, Hilbert space 64
Normal element, in C*-algebra 91
Normal operator 84
Normed linear space 4 27
Numerical radius 115
Numerical range 115
Open mapping theorem 22 23
Operator 81
Orthogonal 65
Orthogonal complement 71
Orthonormal 65 79
Orthonormal basis 74—75
Outer function in  172 174
Outer function in  157
Parallelograrn law 66
Partial isometry 95
Piecewlse continuous function 176
Polar decomposition 97 98
Polar form 95
Polarization identity 64
Polynomials, analytic trigonometric 51
Polynomials, trigonometric 51
Positive element, of C*-algebra 94 117
Positive operator 84
Projection 86
Pure isometry 173
Pure isometry, multiplicity 173
Putnam theorem 120
Pythagorean Theorem 66 73
Quasicontinuous function 176
Quasinilpotent operator 133 145
Quotient algebra 43
Quotient C*-algebra 139
Quotient space 20
Radical ideal, of Banach algebra 60
Radon — Nikodym theorem 25 80
Range, of operator 83
Reducing subspace 98
Reflexive Banach spaces 28—30
Resolvent set 41
Riemann — Stieltjes integral 15
Riesz (F. and M.) theorem 154
Riesz functional calculus 60
Riesz representation theorem 72
Riesz theorem 18
Riesz — Markov representation theorem 20
Self-adjoint element, of C*-algebra 91
Self-adjoint operator 84
Self-adjoint subset 46
Semisimple algebra 60
Separating vector 105
Silov boundary 61 164 173
Silov theorem 53
Similarity, of operators 117
Spectral inclusion theorem 179 188
Spectral mapping theorem 45
Spectral measure, scalar 113
Spectral projection 113
Spectral radius 41
Spectral subspace 113
Spectral theorem 93
Spectrum 41
Spectrum operator 85
Square root, of operator 95
State 147
State, pure 147
Stone — Cech compactification 58 59
Stone — Weierstrass theorem 46
Stone — Weierstrass theorem, generalized 50
Strong operator topology 100
Subharmonic function 174
Sublinear functional 11
Subnormal operator 183
Summability, in Banach space 4
Symbol, of Toeplitz operator 184
Symmetric linear transformation see Linear transformation symmetric
Szego theorem 175
Szego — Nagy theorem 173
Tensor product of Banach algebras 62
Tensor product of Banach spaces 31
Tensor product of Hilbert spaces 79
Tensor product of operators on Hilbert spaces 118
Toeplitz matrix 177
Toeplitz operator 177
Uniform boundedness theorem 29
Unilateral shift 96 117 136
Unit ball, of Banach space 10
Unitary element, of C*-algebra 91
Unitary equivalence, of operators 117
Unitary operator 84 117
Volterra integral operator 132
von Neumann double commutant theorem 118
von Neumann theorem 173
von Neumann — Wold decomposition 173
W*-algebra 101
w*-topology 9 30 78
w-topology 29
Weak operator topology 100
Weak topology 9
Weierstrass theorem 48
Weyl theorem 145
Weyl — von Neumann theorem 146
Widom theorem 195 207
Widom — Devinatz theorem 204
Wiener theorem 56
Wiener — Hopf operator 200
Wintner theorem 183
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