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| Gohberg I., Goldberg S. — Basic Operator Theory |
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| Предметный указатель |
 space 269
Absolutely continuous function 140
Adjoint operator 77
Almost periodic function 37
Analytic operator valued function 231
Baire category theorem 277
Banach space 194
Basic system of eigenvectors and eigenvalues 115
Basis, for a vector space 6
Basis, for a vector space, orthonormal 26
Basis, for a vector space, Schauder 201 242
Basis, for a vector space, standard for  22
Bessel’s inequality 25
Biorthogonal system 205
Bounded linear functionals, representation of 201-203
Bounded linear operator 52
Cauchy sequence 9
Cauchy — Schwartz inequality 2
Closed graph theorem 221 278
Closed operator 220
Closed set 19
Closure of a set 19
Codimension 243
Compact operator 83
Compact operator, characterization of 187
Compact operator, function of 160
Compact operator, normal, characterization of 183
Compact operator, self adjoint, characterization of 113
Compact operator, spectrum of 248
Compact set 261
Complement of a subspace 205 225
Complete inner product space 9
Complete normed linear space 194
Complete orthonormal system 28
Complex n-space 1
Conjugate of an operator 245
Conjugate space of  201
Conjugate space of ![$L_p[a, b]$](/math_tex/68bc2bc72c9fabc3bd8cc413097bfb0082.gif) 202
Continuity of an operator 57
Contraction 256
Contraction mapping theorem 256
Convergence of a sequence 8
Convex set 19
Countable set 265
Diagonalization, simultaneous 181
Differential equation 257
Differential equation in Hilbert space 165
Differential operators 140—147
Dimension of a vector space 6
Dini’s theorem 135
Direct sum 205
Distance from a point to a subspace 10
Distance from a point to a subspace, formula for 14
Eigenvalues, eigenvectors 106
Eigenvalues, eigenvectors of operators of finite rank 108
Eigenvalues, eigenvectors, basic system of 115
Eigenvalues, eigenvectors, simple 145
Equivalent norms 197 222
Essentially bounded function 270
Finite dimensional space, characterization of 198 199
Finite rank operator 63
Finite rank operator, approximation by 241
Finite rank operator, decomposition of 240
Fixed point 255
Fourier coefficient 26 30
Fourier series 30
Fredholm alternative 245
Function of a compact self adjoint operator 160
Gram determinant 13
Gram — Schmidt orthogonalization procedure 21
Graph of an operator 220
Green’s function 140 143
Hadamard’s inequality 15
Hahn — Banach theorem 203 276
Harmonic oscillation, simple 155
Hilbert Schmidt theorem 132
Hilbert space 9
Holder’s Inequality 271
Image of an operator 63
Imaginary part of an operator 182
Implicit function theorem 259
Incompatible systems of equation 16
| Infective 65
Inner product 7
Inner product space 7
Integra-differential equation 168
Integral equation of the second kind 74 179
Integral operator 56 212
Integral operator, adjoint of 77
Interior point 277
Invariant subspace 88
Inverse of an operator 65 70
Inverse of an operator, approximation of 215
Invertible operator 65
Invertible operator of finite rank 66
Isometry 184
Iterative methods 174
Kernel function 56
Kernel of an operator 65
Kronecker delta 32
Lebesgue dominated convergence theorem 269
Lebesgue dominated convergence theorem, integrability 268
Lebesgue dominated convergence theorem, measure zero 267
Matrix representation of an operator 59 211
Mercer’s theorem 136
Metric space 261
Min.-max. theorem 122
Multiplicity of an eigenvalue 117
Non-negative operator 121
Norm 7 194
Norm of an operator 52
Normal operator 183
Normed linear space 194
Normed linear space, complete 194
One-one operator 65
Orthogonal complement 21
Orthogonal projection 82
Orthogonal vectors 10
Orthonormal basis 26
Orthonormal basis, examples of 27
Orthonormal basis, stability of 33
Orthonormal system 10
Oscillating string, displacement of 155
Parallelogram law 8
Parseval’s equality 27
Partially ordered set 273
Positive operator 121
Projection 225
Projection of a vector 35
Pythagorean Theorem 10
Range of an operator 63
Rank of an operator 63
Real part of an operator 182
Regular point 226
Resolvent 231
Resolvent set 226
Riesz representation theorem 61
Schauder basis 201 242
Schwarz inequality 8
Self adjoint operator 81
Self adjoint operator, compact 113
Self adjoint operator, normal 183
Separable Hilbert space 34 265
Separable Hilbert space, normed linear space 200
Shift operator, left, right 56
Span of a set 6
Spectral theorem for compact normal operator 183
Spectral theorem, for compact self adjoint operator 113 118
Spectrum of an operator 226
Sturm — Liouville system 142
subspace 6
Subspace, invariant 88
Surjective 70
Toeplitz matrix 60
Totally ordered set 273
Triangle inequality 8
Uniform boundedness principle 223
Unitary operator 185
Vector space 6
Volterra integral operator 230
Weierstrass approximation theorem 28
Weierstrass approximation theorem, second approximation theorem 29
with external force 157
wronskian 143
Zorn’s Lemma 273
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