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Авторизация |
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Поиск по указателям |
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Abramovich Y.A., Aliprantis C.D. — An Invitation to Operator Theory |
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Предметный указатель |
-space 94 101
-compact operator 401
-space 94 101
-space, complex 106
-space, with unit 94
, band generated by 20
, extended continuous functions 115
, functions vanishing at oo 406
, defect of operator 155
, order dual of 21
, ideal generated by 20
258
-space 85
-space 122
52
-sum of Banach spaces 472
210
210
-space 122
, space of square matrices 318
, nullity of operator 155
, eigenspace with eigenvalue 384
-norm of operator 22
, essential spectral radius of 302
, the double adjoint of operator 4
, the adjoint of operator 4
, , , closed unit balls 3
, double norm dual of 3
, norm dual of 3
, convergence along an ultrafilter 38
, ultrapower of -space 40
, super right-commutant of 399
, ascent of operator 80
, descent of operator 80
, semi — Fredholm operators 166
, super left-commutant of 399
-sum of Banach spaces 281
-sum of Banach spaces 472
, complex numbers 2
, the natural numbers, 2
, the rational numbers 2
, the real numbers 2
, the integers 2
-invariant subspace 387
, algebra generated by 387
, the orbit of under 387
-invariant collection 410
, finite-rank operators from to 125
, Fredholm operators 163
472
, compact operators from to 89
, bounded operators on 2
, bounded operators from to 2
, order bounded operators from to 15
, regular integral operators from to 188
, regular operators from to 14
, vector sublattice generated by 233
-limit of sequence 38
, weakly compact operators from to 89
, the Calkin algebra 299
-integral operators 193 430
, -finite-rank operators 125
-Dedekind complete Riesz space 16
-order closed set 18
-order complete Riesz space 16
-order continuous function 18
, spectrum of operator 238
, approximate spectrum of 249
, continuous spectrum of 249
, essential spectrum of 299
, point spectrum of 248
, residual spectrum of 248
, Weyl spectrum of 312
, norm of set 410
A.e. equal functions 52
Absolute 187
Absolute integral operator 187
Absolute value of vector 15
Abstract integral operator 193 368 430
Additive semigroup 409
Adjoint operator 4 244
Adjoint operator, Hilbert space 453
Algebra 3 386
Algebra of operators 386
Algebra of operators, generated by a sot 387
Algebra of operators, non-transitive 387 440
Algebra of operators, transitive 387
Algebra, 387
Algebra, Calkin 299
Algebra, closed 387
Algebra, dual 387
Algebra, generated by set of operators 387
Algebra, non-transitive 387 440
Algebra, transitive 387
Algebra, unital 3 386 387
Algebraic complement of subspace 169
Algebraic homomorphism 14-1
Almost essentially disjoint operators 477
Almost integral operator 193 430
Analytic function 45
Annihilator 8
Annihilator, of a set 328
Annihilator, of a vector subspace 8 328
Annulus 49
Antisymmetry 13
Approximate eigenvalue 249
Approximate point spectrum 249
Approximation property 125
Archimedean ordered vector space 15
Ascent of operator 80 270
atom 86
Atomic measure space 193
Atomless Riesz space 86
Automatic continuity 147 154
Averaging operator 213
Averaging property 213
Backward shift operator 251
Banach function space 194
Banach function space, associated with or 194
Banach function space, rearrangement invariant 223 494
Banach lattice 22
Banach lattice, AL 94
Banach lattice, AM 94
Banach lattice, complex 105
Banach lattice, with order continuous norm 84
Banach space 2
Banach space, direct sum 5 10
Banach space, function 194
Banach space, locally uniformly convex 460
Banach space, quotient 8
Banach space, reflexive 465
Banach space, uniformly convex 12 457 465
Banach space, uniformly rotund 457
Banach space, uniformly smooth 457
Banach — Steinhaus theorem 4
Band 20
Band irreducible operator 349
Band preserving operator 112
Band projection 21
Band, generated by a set 20
Band, of abstract integral operators 193 430
Band, of integral operators 188
Band, principal 20 118
Band, projection 21
Basic sequence 30
Basic sequence, unconditional 35
Basis 28 436
Basis constant 29
Basis problem 28
Basis, in 36
| Basis, monotone 29
Basis, normalized 29
Basis, unconditional 32 500
Biorthogonal functional 31
Bishop operator 451
Bistochastic projection 221
Bound 15
Bound, greatest lower 15
Bound, least upper 15
Bound, lower 15
Bound, upper 15
Bounded function 64
Bounded function, from above 64
Bounded operator 2
Bounded operator, from below 69
Calkin algebra 299
Canonical projection 299
Caratheodory extension of measure 61
Caratheodory’s theorem 61
Carleman operator 192
Carrier of ideal 27
Carrier of ideal, in 60
Cayley — Hamilton theorem 318
Center of Banach function space 209
Center of Banach lattice 112
Center of Banach lattice, trivial 116
Central operator 112
Cesaro operator 247 450
Chain of open sets 51
Characteristic polynomial 317 327
Characteristic polynomial, of operator 321
Characterization of narrow operator 494
Closed algebra 387
Closed graph theorem 5
Closest point to a set 12
Codimension of vector subspace 155
Cofinal set 66
Collection, strictly transitive 387
Collection, transitive 387
Commutant 138 357 388 398 410
Commutant, of family of operators 410
Commutant, super left, 399
Commutant, super right, 399
Commutator of two operators 398
Compact operator 88 272
Compact-friendly operator 425
Complement, algebraic of subspace 169
Complement, of a closed subspace 386
Complemented subspace 134 386 486
Complete measure 66
Completely continuous function 444
Completion, Dedekind 26
Completion, Maeda — Ogasawara — Vulikh 116
Completion, universal 116
Complex -space 106
Complex Banach lattice 105
Complex lattice isometry 105
Complexification 5
Complexification, of Banach lattice 105 110
Component of a vector 16
Composition operator 142 378
Conditional expectation of function 212
Conditional expectation operator 212
Cone 14 440
Cone, generated by a basis 437 440
Cone, generating 14
Conjugate of matrix 317
Continuous spectrum 249
Contraction 78
Control function 315
Convergence 67
Convergence, 67
Convergence, convergence, of Laurent series 49
Convergence, in measure 53
Convergence, notions in 209
Convergence, order 16
Convergence, pointwise 53
Convergence, uniform 53
Convergence, weak 3
Convergence, weak 3
Convolution of kernels 210
Corank of operator 155
Countable sup property 22 354
Cyclic point of a set 288
Cyclic set 288
Cyclic vector 328 383
Daugavet equation 456 470
Daugavet property 467 473
Decreasing net 16
Dedekind complete Riesz space 15
Dedekind completion 26
Defect of operator 155
Derivative of a function 45
Descent of operator 80 270
Diagonal matrix 118
Diagonal part of operator 117
Diagonal projection 117
Diagonal property 56
Diagonalizable matrix 319
Diagonalizing matrix 319
Differentiable function 45
Direct sum Banach space 10
Direct sum normed space 5
Direct sum of Banach spaces 247
Direct sum of operators 393
Direct sum operator 247
Direct sum property 208
Dirichlet’s Theorem 236
Discrete vector 86
Disjoint complement 21
Disjoint operators 16
Disjoint operators, almost essentially 477
Disjoint operators, essentially 477
Disjointly strictly singular operator 178
Disk 44
Domain of analyticity of function 258
Domination of operators 89 109
Double adjoint 4
Double dual 3
Doubly power bounded operator 247 450
Dual 3
Dual algebra 387
Dual, double 3
Dual, Kther 198
Dual, norm 3
Dual, order 21
Dual, order continuous 21 193
Dual, second 3
Dunford — Pettis operator 409 498
Dunford — Pettis property 360
Eigenspace 384
Eigenvalue 248
Eigenvalue, approximate 249
Eigenvector 248
Entire function 47
Equation, Daugavet 456
Equimeasurable functions 223 494
Essential property 299
Essential singularity 264 270
Essential spectral radius 302
Essential spectrum of an operator 299
Essential sup 64
Essential sup norm 64
Essential upper bound 64
Essentially bounded function 64
Essentially bounded function, from above 64
Essentially disjoint operators 477
Essentially invertible operator 299
Essentially quasinilpotent operator 302
Euclidean norm 316 321
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