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Halmos P.R. — Hilbert Space Problem Book
Halmos P.R. — Hilbert Space Problem Book

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Название: Hilbert Space Problem Book

Автор: Halmos P.R.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1994

Количество страниц: 296

Добавлена в каталог: 30.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$W_k$      211
$\sigma$-field      Prefrase
$\sigma$-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 $H^2$      35
Analytic element of $L^2$      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 $A^2$      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 $B_1(H)$      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 $H^2$      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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