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| Авторизация |
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| Abramovich Y.A., Aliprantis C.D. — An Invitation to Operator Theory |
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| Предметный указатель |
Euclidean norm, of matrix 318
Euclidean topology 321
Expanding operator 350
Exposed point 490
Exposing linear functional 490
Extremally disconnected space 96
Extreme point 490
Factorization of an operator 477
Family of operators, finitely quasinilpotent at a point 410
Family of operators, non-transitive 410
Family of operators, quasinilpotent at a point 410
Family of operators, transitive 410
Fatou property 65
Fatou property,  65
Filter 37
Filter, Fr chet 38
Finite Dimensional Separation Theorem 13
Finite quasinilpotence 410
Finite-rank operator 91 124 430 471
Finite-rank operator, rank 124
Finite-rank operator, representation 124
Fixed ultrafilter 38
Flat of a function 432
Frchet differentiability of the norm 466
Frchet filter 38
Fredholm alternative 169
Fredholm operator 156
Fredholm spectrum 299
Free ultrafilter 38
Fubini’s Theorem 63
Function space 194
Function space, normal 194
Function,  -order continuous 18
Function, analytic 45
Function, bounded 64
Function, completely continuous 444
Function, control 315
Function, defining an integral operator 181
Function, differentiable at a point 45
Function, entire 47
Function, essentially bounded above 64
Function, harmonic 236
Function, holomorphic 45
Function, index 163
Function, jointly measurable 63
Function, measurable 52
Function, onto 69
Function, order continuous 18
Function, resolvent 238 245
Function, retraction 13
Function, state 315
Function, surjective 69
Function, weakly analytic 47
Functional calculus 258
Functional, biorthogonal 31
Functional, multiplicative 148
Functional, supporting 466
Gantmacher’s theorem 89
Gateaux differentiability of the norm 466
Generalized Harris operator 434
Generating cone 14
Graph of function 4
Haar system 36
Harmonic function 236
Harris operator 370
Hereditarily indecomposable B-space 177
Hermitian matrix 317
Hilbert space adjoint 453
Hilbert — Schmidt operator 193
Holomorphic function 45
Homogeneity of the norm 2
Homomorphism, algebraic 144
Homomorphism, lattice 88
Hyperinvariant subspace 348 381
Ideal 20 110
Ideal irreducible operator 111 349
Ideal irreducible semigroup 415
Ideal reducible semigroup 415
Ideal, generated by a set 20
Ideal, null 119 348 399 408
Ideal, null of an  -seminorm 122
Ideal, null of functional 27
Ideal, operator 472
Ideal, principal 20 95 119
Ideal, range of operator 399 408
Ideal, semigroup 417
Implication scheme 351
Indecomposable matrix 333
INDEX function 163
Index of nilpotence 82 323
Index of operator 155
Index theorem 158
Inequality, Jensen 227
Inequality, triangle 2
Infimum 15
Inner product preserving matrix 317
Input-output matrix 315
Integral, integral operator 102 180
Integral, iterated 62
Internal point 101
Interpolation space 224
Interval preserving operator 24 154
Invariant measure 355
Invariant subspace 10 348 381
Invariant subspace problem 381
Invertible operator 10 298
Irreducible matrix 333
Isolated point of the spectrum 265
Isometric normed spaces 2
Isometry 2 11
Isometry, lattice 23 105
Isometry, linear 2 11
Isomorphic Banach spaces 71
Isomorphism between Banach spaces 71
Iterated integral 62
Jensen’s Inequality 227
Joint spectral radius 425
Jointly measurable function 63
Jordan contour 257
Jordan contour, surrounding a set 257
Jordan form of a matrix 326
K the dual 198
Kadets — Klee property 465
Kantorovich — Banach space 85
Kernel of integral operator 181
Kernel operator 181
Krein operator 350 371
Krein — Rutman theorem 277
Kronecker’s theorem 291
Laplace equation 236
Lattice homomorphism 23 88 154
Lattice hyperinvariatr subspace 348 381
Lattice isometric Banach lattices 23
Lattice isometric complex  -lattices 105
Lattice isometry 23 105
Lattice isometry, complex 105
Lattice isomorphism 23
Lattice operations 15
Lattice seminorm 22
Lattice-subspace 229
Laurent series 49
Laurent series expansion 266
Laurent series, expansion of function 49
Limit,  38
Limit, functional 155
Limit, order 17
Linear functional, exposing a point 490
Linear functional, strongly exposing a point 490
Linear isometry 2 11
Linear operator 2
| Liouville number 451
Liouville’s theorem 47
Local quasinilpotence 357 410
Locally uniformly convex -space 460
Lomonosov operator 396
Maeda — Ogasawara — Vulikh completion 116
Majorizing vector space 96
Mapping, nearest point 12
Mapping, quotient 8
Mapping, sublinear 149
Markov matrix 103 332
Markov operator 100
Markov projection 213
Matrix, diagonal 118
Matrix, diagonalizable 319
Matrix, diagonalizing 319
Matrix, hermitian 317
Matrix, indecomposable 333
Matrix, inner product preserving 317
Matrix, input-output 315
Matrix, irreducible 333
Matrix, Markov 103 332
Matrix, non-negative 329
Matrix, norm preserving 317
Matrix, orthogonal 317
Matrix, permutation 333
Matrix, positive 329
Matrix, positive semidefinite 319
Matrix, primitive 343
Matrix, production 315
Matrix, reducible 333
Matrix, representing 321
Matrix, stochastic 103
Matrix, strictly positive 329
Matrix, strongly positive 329
Matrix, symmetric 317
Matrix, unitary 317
Matrix, upper triangularizable 326
Matrix, upper triangularizing 326
Mazur’s lemma 30
Measurable function 52
Measure 61
Measure convergence 53
Measure of non-compactness of operator 309
Measure of non-compactness of set 309
Measure, atomic 193
Measure, complete 66
Measure, invariant 355
Measure, non-atomic 479
Measure, on a semiring 61
Measure, product 62
Minimal polynomial 327
Mixed norm 210
Miyajima projection 235
Modulus 16 104 107
Modulus, of integral operator 102 186 187
Modulus, of operator 16 96 107 113
Modulus, of vector 104
Monotone basis 29
Morera’s theorem 50
Multiplication operation 3
Multiplication operator 136
Multiplicative functional 148
Multiplicative operator 144
Narrow operator 494
Nearest point mapping 12
Nearest point to a set 12
Negative part of vector 15
Neighborhood of set 257
Net 16
Net, decreasing 16
Net, order convergent 16
Neumann series 239
Nilpotent operator 82 244 323
Non-atomic measure 479
Non-atomic Riesz space 86
Non-negative matrix 329
Non-quasianalytic 450
Non-scalar operator 383
Non-transitive algebra 387 440
Non-transitive family of operators 410
Non-trivial vector subspace 348 381
Norm 2
Norm dual 3
Norm preserving matrix 317
Norm, essential-sup 64
Norm, Euclidean 316 321
Norm, Frchet differentiable 466
Norm, Gateaux differentiable 466
Norm, mixed 210
Norm, of a set 410
Norm, of integral operator 102
Norm, of matrix 318
Norm, order continuous 84
Norm, quotient 8
Norm, strictly monotone 216
Norm, sup 64
Norm, uniformly convex 12
Normal function space 194
Normal integral 198
Normal operator 453
Normal Riesz space 21 193
Normalized basis 29
Normed function space 194
Normed Riesz space 22
Normed space 2
Normed space, function 194
Norming subspace 51
Null ideal 27 348 399 408
Null ideal, of -seminorm 122
Null ideal, of functional 119
Null space of operator 79 155
Nullity of operator 155
Onto function 69
Open disk 44
Open mapping theorem 4
Operation, multiplication 3
Operator 2
Operator domination 89 109 425
Operator ideal 472
Operator norm 2
Operator norm of matrix 318
Operator of rank  124
Operator,  -compact 401
Operator,  258
Operator, abstract integral 193 368 430
Operator, adjoint 4 244 453
Operator, almost integral 193 430
Operator, averaging 213
Operator, backward shift 251
Operator, band irreducible 349
Operator, band preserving 112
Operator, Bishop 451
Operator, bounded 2
Operator, bounded below 69
Operator, Carleman 192
Operator, central 112
Operator, Cesaro 247 450
Operator, compact 88 272
Operator, compact-friendly 425
Operator, composition 142 378
Operator, conditional expectation 212
Operator, disjointly strictly singular 178
Operator, double adjoint 4
Operator, doubly power bounded 247 450
Operator, Dunford — Pettis 409 498
Operator, Eredholm 156
Operator, essentially invertible 299
Operator, essentially quasinilpotent 302
Operator, expanding 350
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