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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 |
Series of vectors 49
Sesquilinear form 1 2
sgn Prefrase
Shields, A.L. 28 68 69 85
Shift 89 143 153
Shift as universal operator 151
Shift, bilateral 84
Shift, invariant subspace 156 157
Shift, modulo compact operators 184
Shift, monotone 191
Shift, multiplicity 151
Shift, polynomials in 198
Shift, simple 151
Shift, square root 145 147 151
Shift, unilateral 82
Shift, weighted 89 90 91 92 93 94 95 96 98 102 104 139 159
Signum Prefrase
Similar normal operators 192
Similar operators 75
Similar subnormal operators 199
Similarity and spectrum 75
Similarity of weighted shifts 90
Similarity to contractions 154
Similarity to parts of shifts 153
Similarity, topological properties 101
Simple curve 5
Simple function 173
Simple unilateral shift 151
Singular operator 100
Skew-symmetric Volterra operator 189
Sliding product 91
SOT 107
span Prefrase
Spec 73
Special invariant subspaces of the shift 156
Spectra and conjugation 73
Spectral inclusion theorem 200 201
Spectral inclusion theorem for Toeplitz operators 245
Spectral mapping theorem 74 123
Spectral measure 5 142
Spectral measure of the unit disc 194
Spectral parts of a diagonal operator 80
Spectral parts of a multiplication 81
Spectral radius 88 91 153
Spectral radius of a weighted shift 91 95
Spectral radius, continuity 104
Spectral radius, subadditivity 88
Spectral radius, submultiplicativity 88
Spectral set 229
Spectral theorem 73 121 123
Spectral theorem, avoidance 123 124
Spectral theory 73
Spectraloid operator 219
Spectrum 67 73
Spectrum and numerical range 214
Spectrum and similarity 75
Spectrum of a commutator 235
Spectrum of a diagonal operator 63
Spectrum of a direct sum 98
Spectrum of a functional multiplication 85
Spectrum of a Hermitian Toeplitz operator 250
Spectrum of a multiplication 67
Spectrum of a partial isometry 133
Spectrum of a product 76
Spectrum of a Toeplitz operator 247 248 250
Spectrum of the bilateral shift 84
Spectrum {1}, norm 1 190
Spectrum, continuity 102 105 106
Spectrum, non-empty 87
Spectrum, normal continuity 105
Spectrum, one-point 96
Spectrum, perturbed 183
Spectrum, semicontinuity 103
Spectrum, strong semicontinuity 119
Square root 121
Square root of a compact operator 178
Square root of a shift 145 147 151
Square root, continuity 126
Square-summable Taylor series 35
Squaring, continuity 111
Squaring, weak sequential continuity 114
Stampfli, J.G. 203 221
Strict, contraction 153
Strict, convexity 4
Strict, positiveness 2
Strong bounded continuity of multiplication 117
Strong boundedness 51
Strong closure and extension 225
Strong closure of co-isometries 225
Strong closure of hyponormal operators 226
Strong closure of projections 225
Strong closure of unitary operators 225
Strong convergence 19
Strong density of nilpotents 111 225
Strong dilation 227
Strong normal continuity of adjoint 116
Strong operator convergence 118
Strong operator topology 107
Strong semicontinuity of spectrum 119
Strong topology 19
Structure of set of eigenvectors 83
Subadditivity of spectral radius 88
Submultiplicativity of spectral radius 88
Subnormal idempotent 208
Subnormal operator 195
Subnormal operators, similarity 199
Subnormal partial isometry 204
Subnormal versus hyponormal 203 209
Subnormal versus quasinormal 195
Subnormality and numerical range 217
subspace Prefrase 13
Subspace, invariant 156 157 191 196
Subspace, projection image 223
Subuniform convergence Prefrase
Support 96
Supremum 14
Symmetric sesquilinear form 2
Symmetric transformation 60
Symmetry 143
Szego kernel 37
T-total set 11
Taylor series Prefrase
Thompson, J.G. 145
Toeplitz matrix 242
Toeplitz operator Prefrase 242
Toeplitz operator, analytic 242 247
Toeplitz operator, co-analytic 243
Toeplitz operator, Hermitian 245 248 250
Toeplitz operator, numerical range 245
Toeplitz operator, quasinilpotent 245
Toeplitz operator, spectral inclusion 245
Toeplitz operator, spectrum 247 248 250
| Toeplitz products 243
Toeplitz products, compact 244
Toeplitz products, continuous 246
Toeplitz — Hausdorff theorem 210
Topological vector space 8
Topologies for operators 107
Total set 8
Total set, minimal 11
Total set, orthonormal 55
Totality of cyclic vectors 156
Totally total sets 11
tr Prefrase 211
Trace Prefrase 211 230 234 236
Triangular matrix 167
Triangular matrix, plus one 167
Trigonometric polynomial 33 41 165
Two-sided ideal 170 177
Tychonoff — Alaoglu theorem 23
Unbounded analytic function with bounded real part 43
Unbounded symmetric transformation 60
Unbounded vector 30
Unbounded Volterra kernel 187
Uncertainty principle 230
Uniform boundedness principle 27 29 30 49 51 60 88 113
Uniform, strong convergence 107
Uniform, topology 107
Uniform, weak convergence 107
Unilateral shift 82 128 149 160 162 168 198 209
Unilateral shift of higher multiplicity 151
Unilateral shift, commutant 147 148
Unilateral shift, distance to normal operators 144
Unilateral shift, distance to unitary operators 150
Unilateral shift, imaginary part 144
Unilateral shift, invariant subspaces 156 157
Unilateral shift, numerical range 212
Unilateral shift, real part 144
Unilateral shift, simple 151
Unilateral shift, square root 145 147 151
Unilateral shift, versus normal operators 144
Unilateral shift, wandering subspaces 155
UNIT 230
Unit ball 4
Unit ball, weak metrizability 24
Unit disc 4
Unit disc, spectral measure 194
Unit sphere 4 25 107
Unit sphere, weak closure 25
Unit vector 4
Unitary equivalence 6
Unitary equivalence of partial isometries 132
Unitary equivalence of similar normal operators 192
Unitary equivalence of similar subnormal operators 199
Unitary equivalence of weighted shifts 89 90
Unitary operators, distance from shift 150
Unitary operators, strong closure 225
Unitary operators, weak closure 224
Unitary, dilation 222
Unitary, multiplicative commutator 239
Unitary, power dilations 227
Upper semicontinuity 21 103
Upper semicontinuity of spectrum 103
Vandermonde 10
Vasunin, V.I. 163
Vector sum 13
Vector sum, closed 15
Vector sum, non-closed 13 14 52
Volterra integration operator 188 191 215
Volterra integration operator, numerical range 210
Volterra kernel, bounded 186
Volterra kernel, unbounded 187
Volterra operator 186 187 188
Volterra operator, skew-symmetric 189
von Neumann algebra 122
Von Neumann’s inequality 229
w 218
Wallen, L.J. 8 92
Wandering subspace 155 157
Wasiutynski, C. 103
Weak analyticity 86
Weak boundedness 27
Weak Cauchy net and sequence 30
Weak closure and dilation 224
Weak closure of a subspace 19
Weak closure of normal operators 224
Weak closure of projections 224
Weak closure of unit sphere 25
Weak closure of unitary operators 224
Weak compactness of the unit ball 23
Weak completeness 30
Weak continuity 19
Weak continuity of norm and inner product 20
Weak convergence of orthonormal sequences 19 20 25
Weak convergence of projections 115
Weak discontinuity of norm 20 21
Weak metrizability and separability 26
Weak metrizability of Hilbert space 28
Weak metrizability of the unit ball 24
Weak operator topology 107
Weak separability 22
Weak sequential, closure 25 224
Weak sequential, continuity of squaring 114
Weak topology 19
Weak topology of Banach spaces 107
Weak* compactness 23
Weakly bounded set 51
Weakly closed linear manifold 19
Weakly complete Hilbert space 30
Weakly dense set 25
Weakly open set 19
Weakly separable Hilbert space 22
Weierstrass approximation theorem Prefrase 33 126 137 165 246
Weighted sequence space 95
Weighted shift 89 90 92 94 95 96 98 102 104 139 159
Weighted shift, approximate point spectrum 94
Weighted shift, eigenvalues 93
Weighted shift, norm 91
Weighted shift, quasinormal 139
Weighted shift, spectral radius 91 95
Weighted shifts, similarity 90
Weighted shifts, unitary equivalence 89 90
Weiss, G.L. 56
Weyl’s theorem 182 184
Wielandt’s proof 230
Wiener, N. 12
Wintner, A. 219
Wintner’s proof 230
Wiser, R.F. 9
WOT 107
x-axis 52 53
Zero-divisor 158 243 249
Zero-divisor, modulo compact operators 64
Zorn, M.A. 70
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