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| Авторизация |
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| Поиск по указателям |
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| Halmos P.R. — Hilbert Space Problem Book |
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| Предметный указатель |
Invertible operators 100
Invertible operators, connectedness 141
Invertible operators, density 140
Invertible operators, openness 100
Invertible sequence 63
Invertible transformation 52
Involution 143
Isometry 127
Isometry, characterization 149
Isometry, pure 149
Jacobi matrix 44
Joint continuity 111
k-numerical range 211
Kakutani shift 106
Kakutani, S. 104
Kaplansky, I. 232
Kelley, R.L. 90 159
Ker Prefrase
Kernel Prefrase
Kernel of an integral operator 173
Kernel, function 37
Kernel, product 186
Kernel, Volterra 186
Kleinecke — Shirokov theorem 232 233
Kronecker delta 37
Large subspace 142 234
Lattice 191
Lattice of subspaces 14
Lattice, distributive 14
Lattice, modular 14
Laurent, operator and matrix 241 245
Laurent, series Prefrase
Law of nullity 151
Least upper bound 14
Lebesgue, bounded convergence theorem 41
Lebesgue, dominated convergence theorem Prefrase 148 228
Lebow, A. 111
Left divisibility 59
Left invertibility 144
Left invertible operators 140
Left shift 143
Leibniz formula 232
Lim 105
Liminf 105
Limit of commutators 231 235
Limit of operators of finite rank 175
Limit of quadratic forms 1
Limsup 103 105
Lindelof space Prefrase 123
Linear basis 7
Linear dimension 7
Linear functional 3
Linear functional on  29
Linear manifold 13 54
Liouville’s theorem 87
Local compactness and dimension 16
Locally finite measure 64
Lower semicontinuity 21
Lower semicontinuity of operator norm 109
Lumer, G. 102
Majorization 59
Matrix 44 70
Matrix, bounded 47
Matrix, products 186
Maximal orthonormal set 54 55
Maximal partial isometry 128 136
Maximal polar representation 135
Maximum Modulus Principle Prefrase 41
McCarthy, C.A. 114
McLaughlin, J.E. 70
Mean ergodic theorem 228
Measure in Hilbert space 18
Metric, space of operators 99
Metric, topology 19
Michael, E.A. 222
Minimal normal extension 197
Minimal total set 11
Mixed continuity 169
Mixed Schwarz inequality 138
Modular lattice 14
Modular law 15
Monotone shift 191
Multiple 157
Multiplication 64 56 67 123
Multiplication in  34
Multiplication on 62
Multiplication on a functional Hilbert space 68
Multiplication, continuity 111
Multiplication, norm 64
Multiplication, separate continuity 112
Multiplication, sequential continuity 113
Multiplication, spectral parts 81
Multiplication, strong bounded continuity 117
Multiplicative commutator 238
Multiplicative commutator, unitary 239
Multiplicativity of extension 42
Multiplicity of shift 151
Multiplicity, theory 146
Multiplier 65 69
Multiplier of functional Hilbert space 69
Muntz — Szasz theorem 165
Net 1
Nikolskii, N.K. 163
Nilpotent 97 104
Nilpotent, strong density 111 225
Non-closed range 52
Non-closed vector sum 13 14 52
Non-commutative approximation theory 185
Non-cyclic operator 162
Non-emptiness of spectrum 87
Non-overlapping chords 5
Non-separable Hilbert space 54
Non-tangential convergence 40
Nordgren, E.A. Prefrase 103
Norm 1, spectrum {1} 190
Norm, continuity 108
Norm, of a linear transformation 51
Norm, of a multiplication 64
Norm, of a weighted shift 91
Norm, of the Volterra integration operator 188
Norm, power and power norm 205
Norm, topology 19 107
Norm, upper semicontinuity 21
Norm, weak continuity 20
Norm, weak discontinuity 20 21
Normal and subnormal partial isometries 204
Normal continuity of spectrum 105
Normal dilation 222
Normal extension, minimal 197
Normal operators, algebras 193
Normal operators, compact 172
Normal operators, distance from shift 144
Normal operators, partial isometries 204
Normal operators, reducing subspaces 142
Normal operators, spectral mapping theorem 123
Normal operators, versus unilateral shift 144
Normal operators, weak closure 224
Normality and numerical range 216
Normalized crinkled arc 6
Normaloid operator 219
Normed algebra 230
NOT 107
NULL 151
Null point 68
NULL-SPACE Prefrase
Nullity 130 151 181 230
Numerical radius 218
Numerical range 210
Numerical range and normality 216
Numerical range and quasinilpotence 215
| Numerical range and spectrum 214
Numerical range and subnormality 217
Numerical range of a compact operator 213
Numerical range of a Toeplitz operator 245
Numerical range of the unilateral shift 212
Numerical range of the Volterra integration operator 210
Numerical range, closure 212
Numerical range, continuity 220
Numerical range, higher-dimensional 211
Odd function 189
One-point spectrum 96
Open unit ball 4
Openness of invertible operators 100
Operator Prefrase
Operator with large kernel 234
Operator, determinant 70 71 72
Operator, determinant with finite entry 72
Operator, determinant, commutative 70
Operator, matrix 70 71 72
Operator, space, separability 99
Operator, topologies 107
Orbit 168
Order for partial isometries 128
Orthogonal dimension 7 54
Orthonormal basis 7
Orthonormal sequences, weak convergence 19 20 25
Orthonormal set 55
Paley, R.E.A.C. 12
Paley-Wiener 12
Parrott, S.K. 201
Parseval’s identity 12 34 174
Part of an operator 152
Partial isometries, closure 129
Partial isometries, components 131
Partial isometries, connectedness 129
Partial isometries, unitary equivalence 132
Partial isometry 127
Partial isometry, maximal 128 136
Partial isometry, normal 204
Partial isometry, spectrum 133
Partial isometry, subnormal 204
Parts of shifts 153
Pearcy, C.M. Prefrase
Peller, V.V. 163
Perturbation 182
Perturbation of spectrum 106 183
Perturbation, quasinilpotent 106
Point evaluation 31
Point spectrum 73
Polar decomposition 56 134 135 170 175 211
Polar representation, maximal 135
Polarization 1
Polynomially diagonal operator 125
Polynomials in the shift 198
Position operator 165 199
Positive self-commutator 236
Positive sesquilinear form 2
Positivity of Hilbert matrix 48
Poulsen, Frode D. 187
Power of the continuum 54
Power, bounded 154
Power, dilation 227
Power, inequality 221
Power, norm 92 205
Power, series 10 35
Powers of a hyponormal operator 209
Precompact 170
Preservation of dimension 56
Principle of uniform boundedness 27 29 30 49 51 60 88 113
Product in 34
Product of kernels 186
Product of normal operators 192
Product of symmetries 143
Product, matrix 186
Product, topology 23
Projection as self-commutator 237
Projection, dilation 222
Projection, image of a subspace 223
Projection, infimum 122
Projections of equal rank 57
Projections, strong closure 225
Projections, weak closure 224
Projections, weak convergence 115
Proper ideal 176
Pure isometry 149
Putnam — Fuglede theorem 192
Quadratic form 1
Quasinilpotence 96 97 153 179 186 187 188
Quasinilpotence and numerical range 215
Quasinilpotent, analytic 97
Quasinilpotent, hyponormal 205
Quasinilpotent, perturbation 106
Quasinilpotent, Toeplitz operator 245
Quasinormal operator 137 195
Quasinormal operator, idempotent 208
Quasinormal operator, invariant subspaces 196
Quasinormal weighted shift 139
R 88
Radial limit 40
Radius of convergence 35
Ran Prefrase
RANGE Prefrase
Range of a compact operator 180
Range, inclusion 59
Range, non-closed 52
Rank 57 130 152
Rank, finite 169 171 173 175 176 181
Re Prefrase
Real function in 33
Real part of unilateral shift 144
Reducible weighted shift 159
Reducing subspace of a normal operator 142
Region 31
Reparametrization 6
Representation of a linear functional 3
Reproducing kernel 37
Residual spectrum 73
Residual spectrum of a normal operator 79
Resolvent 86 87 88
Riesz representation theorem 3 36
Riesz theorem, F.and M. 55 158
Riesz — Fischer theorem 31
Riesz, F.and M. 158
Right shift 143
Right-invertible operators 140
Ring 70
Ring of operators 122
Rosenthal, P. 179
Sarason, D.E. 27 160 199
Schur test 45
Schwab, D. Prefrase
Schwarz inequality 2
Schwarz inequality, mixed 138
Segment 4
Self-adjoint ideal 170
Self-commutator 236 237
Self-conjugate functional Hilbert space 38
Semicontinuity 21
Semicontinuity of norm 21 109
Semicontinuity of operator norm 109
Semicontinuity of spectrum 103
Semilinear functional 1
Separability and dimension 17
Separability and weak metrizability 26
Separability of B(H) 99
Separable Hilbert space 17 22
Separate continuity of multiplication 112
Sequence space, weighted 95
Sequential continuity of multiplication 113
Sequential weak completeness 30
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