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| Авторизация |
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| Halmos P.R. — Hilbert Space Problem Book |
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| Предметный указатель |
 211
 -field Prefrase
-finite measure space 29
Abnormal 237
Absolutely continuous function 69
Adams, G.T. 28
Adjoint, continuity 110
Adjoint, cyclic vectors 164
Adjoint, linear transformation 51
Adjoint, strong normal continuity 116
Adjoint, weighted shift 93
Algebraic operator 97
Algebras of normal operators 193
Analytic characterization of  35
Analytic element of  33
Analytic function 86 97
Analytic Hilbert space 31
Analytic operator 97
Analytic quasinilpotent operator 97
Analytic resolvent 86 87 88
Analytic Toeplitz operator 242 247
Approximate, basis 12
Approximate, point spectrum 73 77 78
Approximate, point spectrum of weighted shift 94
Approximation theory, non-commutative 185
Atkinson’s theorem 181
Atom of infinite measure 64 68
Attainment of norm 170
Baire category 7 27 52 161
Ball 4
Banach space 8 23 27 52 170
Basis 7
Basis for  32
Basis, boundedness on 50
Basis, compactness on 177
Basis, Hamel 7
Basis, linear 7
Basis, orthonormal 7
Bastian, J.J. 132
Bendixson — Hirsch theorem 214
Berger, C.A. 211 221
Bergman kernel 37
Bessel’s inequality 12
Bilateral shift 84 183 198
Bilateral shift, commutant 146
Bilinear functional 1
Borel set 18
Boundary of spectrum 78
Boundary point 4
Bounded approximation 41
Bounded from below 52 73 144
Bounded linear functional 3
Bounded linear transformation 51
Bounded matrix 47
Bounded real part 43
Bounded Volterra kernel 186
Boundedness of multiplications . 66
Boundedness of multipliers . 65
Boundedness on bases 50
Boundedness, weak 27
Brown, A. 210 220
Calkin algebra Prefrase
Cauchy net and sequence 30
Cesaro, convergence 41 96
Cesaro, matrix 177
Characteristic polynomial 76
Characterization of isometries 149
Chord 5
Circular symmetry 89
Closed graph 29 52 58 59 60 66 68 181
Closed ideal 170
Closed linear manifold Prefrase 13
Closed linear transformation 58
Closed unit ball 4
Closed vector sum 13 15
Closure of approximate point spectrum 77
Closure of numerical range 212
Closure of partial isometries 129
Co-analytic element of L2 33
Co-analytic Toeplitz operator 243
Co-dimension Prefrase
Co-isometries, strong closure 225
Co-isometry 127
Co-nullity 130
Co-range 151
Co-rank 130 181
Co-subnormal operator 203
Column-finite matrix 44
Commutant 146
Commutant of the bilateral shift 146
Commutant of the unilateral shift 147 148
Commutant of the unilateral shift as limit 148
Commutative operator determinants 70
Commutative ring 70
Commutator 230
Commutator, direct sum 235
Commutator, limit 231
Commutator, multiplicative 238
Commutator, subgroup 240
Compact diagonal operator 171
Compact hyponormal operator 206
Compact operator 170
Compact operator, distance from shift 185
Compact operator, numerical range 213
Compact operator, range 180
Compact operator, square root 178
Compact Toeplitz product 244
Compact versus Hilbert — Schmidt 174
Compactness of  107
Compactness on bases 177
Complement of subspace 53
Complete continuity 170
Completeness of B(H) 99
Components of space of partial isometries 131
Compression 222
Compression, spectrum 73
Conjugate class 101
Conjugate function 43
Conjugate linearity 1
Conjugation in functional Hilbert spaces 38
Conjugation, continuity 33
Connectedness of invertible operators 141
Connectedness of partial isometries 129
Continuity of adjoint 110
Continuity of co-rank 130
Continuity of conjugation 33
Continuity of extension 39
Continuity of functional calculus 126
Continuity of inversion 100
Continuity of multiplication 111
Continuity of norm 108
Continuity of nullity 130
Continuity of numerical range 220
Continuity of rank 130
Continuity of set-valued functions 105
Continuity of spectral radius 104
Continuity of spectrum 102 105 106
Continuity of square root 126
Continuity of squaring 111
continuous curve 5
Continuous curve of unitary operators 131
Continuous spectrum 73
Continuous Toeplitz products 246
Continuum 54
Contraction 132 152 153
Contraction, similarity to 154
conv 216
Convergent sequences of sets 105
Convex hull 216
Convexity 4
| Convexoid operator 219
Counting measure 64 173
Cramer’s Rule 70
Crinkled arc 6
Cyclic direct sum 163
Cyclic matrix 167
Cyclic operator 161
Cyclic subspace 165
Cyclic vector 160
Cyclic vectors of adjoints 164
Cyclic vectors of position operator 165
Cyclic vectors, totality 156
Decreasing squares 124
Degree of a vector 191
Dense, linear manifold 54
Dense, orbit 168
Dense, range 73
Density of cyclic operators 161
Density of invertible operators 140
Density of non-cyclic operators 162
Derivation 232
DET Prefrase 70
Determinant Prefrase 70
Determinant, formal 70 71
Determinant, operator 70 71 72
diag 61
Diagonal 61
Diagonal compact operator 171
Diagonal operator, spectral parts 80
Diagonal operator, spectrum 63
Dilation 222
Dilation and weak closure 224
Dilation, power 227
Dilation, strong 227
Dilation, unitary 222
DIM Prefrase
DIMENSION Prefrase 7 11 54
Dimension and local compactness 16
Dimension and separability 17
Dimension, linear 7
Dimension, orthogonal 7 54
Dimension, preservation 56
Diminishable complement 53
Direct sum 70
Direct sum as commutator 235
Direct sum, spectrum 98
Dirichlet, kernel 41
Dirichlet, problem 43
Distance from commutator to identity 233
Distance from shift to compact operators 185
Distance from shift to normal operators 144
Distance from shift to unitary operators 150
Distributive lattice 14
Dominated Convergence Theorem Prefrase 148 228
Donoghue lattice 191
Douglas, R.G. Prefrase 131
Duncan, J. 138
Eigenspace 125
Eigenvalue of Hermitian Toeplitz operator 248
Eigenvalue of weighted shift 93
Eigenvector 83
Elementary symmetric function 106
Ergodic theorem 228
Essential, boundedness 56
Essential, range 67 247
Essential, spectrum Prefrase
Essential, supremum 64
Evaluation functional 36
Even function 189
Exponential Hilbert matrix 47
Extension and strong closure 225
Extension into the interior 35
Extension of a function in 39
Extension of finite co-dimension 202
Extension, continuity 39
Extension, multiplicativity 42
Extreme point 4 136
F.and M.Riesz theorem 55 158 243 248 250
Factorization 59
Fejer, kernel 41
Fejer, theorem 41 165
Field of values 210
Filling in holes 201
Final space 127
Finite rank 169 171 173 175 176 181
FORM 1
Formal determinant 70 71
Fourier expansion 7
Fredholm alternative 179 184 187
Fredholm operator 181
Fuglede theorem 146 192 193 194
Full linear group 240
Functional calculus 97 123 126 131
Functional Hilbert space 36 37 38 68 69 85
Functional multiplication 68 69 85
Gram — Schmidt process 7 17 167
Gramian 48 49
Graph 52 53 54 58
Greatest lower bound 14
Hadwin, D.W. Prefrase
Halmos, P.R. 85
Hamel basis 2 7 30 54
Hamilton — Cayley equation 160
Hankel, matrix 47
Hankel, operator Prefrase
Hardy spaces 33 34 35
Harmonic function 38
Harrison, K.J. 106
Hausdorff metric 220
Heisenberg uncertainty principle 230
Hermitian operators, increasing sequences 120
Hermitian Toeplitz operator 245 248
Hermitian Toeplitz operator, spectrum 250
Higher-dimensional numerical range 211
Hilbert — Schmidt operator 173 174
Hilbert, matrix 46 47 48
Hilbert, transform 43
hole 201
Hyponormal operator 203 206
Hyponormal operator, compact imaginary part 207
Hyponormal operator, idempotent 208
Hyponormal operator, powers 209
Hyponormal operator, quasinilpotent 205
Hyponormal operator, spectral radius 205
Hyponormal operator, strong closure 226
Ideal 170 177
Ideal of operators 176
Ideal, proper 176
Idempotent 208 225
Im Prefrase
Image of subspace 223
Imaginary part of unilateral shift 144
Increasing sequence of Hermitian operators 120
Infimum 14
Infimum of two projections 122
Infinite matrix 44
Infinite Vandermonde 10
Initial space 127
Inner function 157
Inner product, weak continuity 20
Integral operator 173 186 189
Integration operator 188 191
Interior 4
Interior of conjugate class 101
Internal direct sum 70
Invariant subspace of quasinormal operators 196
Invariant subspace of the shift 156 157
Invariant subspace problem 191
Invertible function 67
Invertible modulo compact operators 181
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