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| Eidelman Y., Milman V., Tsolomitis A. — Functional Analysis. An Introduction |
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| Предметный указатель |
Alaoglu 149
Algebra semisimple 181
Algebraic span 185
Almost periodic function 188
Analytic functions 172
Arzell 60
Baire category 128
Baire — Hausdorff 128
Banach algebra 167
Banach limit 163
Banach space 17 127
Banach — Steinhaus 67 135 136
Band matrix 70
Basis 140
Basis of a normed space 31
Basis of space 5
Bessel inequality 29 31
Biorthogonal functionals 139
Biorthogonal system 50
Birkhoff's theorem 155
Bounded functional 38
Bounded set 14
Bounded variation 161
Category 128
Cauchy integral 173
Cauchy sequence 16
Cauchy — Schwartz inequality 10 26
Cayley transform 216
Center of a set 129
Centrally symmetric 14
Closed graph operator 132 133
Closed set 12
Closure 13
Closure of operator 133
Codimension 6
Compact operators 59
Compact set 59
complete 18
Complete space 17
Complete system 29 30
Completion 19 21 117
conjugate 184
Continuous functional 38
Continuous spectrum 76 212
Convex 14 35 144
Convex set 13
Convolution of sequences 169
cosets 5
Decomposition of the identity 109
Dense set 13
Dimension of space 5
Dirac measure 157
Direct decomposition 101
Dirichlet kernel 139
Distance to a set 35
Domain of operator 203
Dual norm 47
Dual operator 63
Dual space 47 51
Eberlain — Schmulian 152
Eigenvalue 75 211
Eigenvalue, multiplicity 76
Eigenvector 212
Embedding operator 60
Equicontinuous 60
Equivalent norms 8
Essential involution 188
Extremal point 153 154
Extremal set 153
Field 171
Finite rank, rank operators 65
Finite support sequence 4
First category set 128
Fisher 93
Fourier transform 121
Fredholm, first theorem 81
Fredholm, second theorem 81
Fredholm, theory 77
Fredholm, third theorem 82
Gelfand 167 171
Gelfand map 176
Gelfand theorem 171
Gelfand — Mazur 176
Gelfand — Naimark theorem 186
Generalized Cauchy — Schwartz inequality 96
Generalized nilpotent 182
Generator of simple spectrum 116
Goldstein 151
Gram-Schmidt 30
Graph method 215
Graph of operator 132
Haar system 162
Hahn — Banach 47 142
Heine — Borel 107
hilbert 3 25
Hilbert space 33
Hilbert — Courant 93
Hilbert — Schmidt, first theorem 90
Hilbert — Schmidt, second theorem 94
Hilbert, space 27 28
Hilbertian norm 27
Holder's inequality 9
Hormander 134
Ideal 170
Image 4
Index of defect 206
Inequality, Cauchy — Schwartz 10 26
Inequality, Cauchy — Schwartz, generalized 96
Inequality, Hoelder 9
Inequality, Hoelder, integral form 10
Inequality, Minkowski 11
Inequality, Minkowski, integral form 12
Inner product 25
Integral representation 173
interval 13
Invariant subspace 87 90
Inverse operator 68
Invertible, element of a Banach algebra 170
Invertible, operator 68
Involution 184
Involution, essential 188
Isometry 19 116
Isometry, into 19
Isomorphism 4
James 153
Kernel 4 15 130
Kernel function 57
Kernel of a set 129
Kernel of an operator 57
Krein — Milman 153 154
Limit along an ultrafilter 193
Linear functional 37
Linear functional, positive 188
Linear map 3
Linear space 3
Linear span 5
Linearly dependent set 5
Linearly dependent vectors 5
Linearly independent 30
Linearly independent relative to subspace 6
Linearly independent vectors 5
Livshic 129
Loranian polynomial 122
Majorizing element 172
Maximal ideal 171
Measure, Dirac 157
Measure, probability 156
| Measure, strongly regular 156
Mercer's theorem 95 96
Minimal system 139
Minimax principle 93
Minkowski's functional 146 147
Minkowski's inequality 11
Multiplicity of the eigenvalue 76
Non-separable 41
Norm 7
Norm, convergence 67
Norm, equivalent 8
Norm, stronger 8
Normed space 7 8 14
Normingset 164
Nowhere dense 128
Open ball 12
Open map 69
Open radius 12
Open set 12
Operator 55
Operator of finite rank 65
Operator self-adjoint 87 204
Operator symmetric 87 204
Operator unitary 116
Operator unitary equivalent 117 224
Operator, compact 59
Operator, domain 203
Operator, graph of 132
Operator, index of defect 206
Operator, isometry 116
Order of self-adjoint operators 96
Orthogonal, complement 36
Orthogonal, decomposition 34 35
Orthonormal system 28
Orthoprojection 101
Pairing 64
Parallelogram law 27 88
ParsevaTs identity 32
Perfectly convex set 129
Point spectrum 75
Polya 138
Polydisc 199
Positive linear functional 188
Precompact, set 59
Precompact, space 60
Probability measure 156
Projection 34
Projection operators 100
Projection spectral family 124
Proper ideal 170 171
Pythagorean Theorem 27
Quotient, normed space 14
Quotient, radical 181
Quotient, space 5 19
Ramsey theorem 194
Rank of an operator 65
Reducing subspace 122
Reflexive space 50
Regular point 75 173
Relatively compact set 59
Residual spectrum 76 212
Riesz representation 40
Scalar product 25
Schauder basis 140
Second category 128
Second category set 128
Self-adjoint, element 185
Self-adjoint, operator 87 204
Semilinearity 25
Seminorm 15
Semisimple algebra 181
Separable space 31
Separation of convex sets 147
Set, center of 129
Set, compact 59
Set, first category 128
Set, kernel of 129
Set, perfectly convex 129
Set, precompact 59
Set, relatively compact 59
Shift operator 58
Simple spectrum 116
Simple spectrum, generator 116
Singular point 174
Space, Banach 17 127
Space, of bounded operators, of maximal ideals 176
Space, reflexive 50
Spectral decomposition 108
Spectral, decomposition 108 217
Spectral, family 109
Spectral, family of projections 124
Spectral, integral 110
Spectral, properties 121
Spectral, theory 75
Spectrum 75 211
Spectrum point 75
Strong convergence 67
Stronger norm 8
Strongly, continuous function 161
Strongly, holomorphic function 161
Strongly, regular measure 156
Sublinear function 142
subspace 4
Subspace, invariant 87
Symmetric algebra 185
Symmetric extension 204
Symmetric kernels 94
Symmetric operator 87 204
system 162
Tensor product 66
Theorem Alaoglu 149
Theorem Banach — Steinhaus 136
Theorem Cauchy 173
Theorem Eberlain — Schmulian 152
Theorem Fredholm, first 81
Theorem Fredholm, second 81
Theorem Fredholm, third 82
Theorem Gelfand 171
Theorem Gelfand — Naimark 186
Theorem Goldstein 151
Theorem Hahn — Banach 47 142
Theorem Hormander 134
Theorem James 153
Theorem Krein — Milman 153 154
Theorem Liouville 175
Theorem Mercer 95
Theorem Polya 138
Theorem Ramsey 194
Theorem Wiener 178
Total set 48
Triangle inequality 7
Uniform convergence 67
Uniformly bounded 60
Unit ball 14
Unit sphere 14 48
Unitary operator 121
Unitary operators 116
Unitary operators equivalent 116 224
Volterra operator 82
Weak convergence 68
Weak topology 148
Weakly continuous function 161
Weakly holomorphic function 161
WeierstralS 30
Wiener algebra 169 178
Wiener theorem 178
Zabreiko 135
Zorn's lemma 154
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