Abramovich Y., Aliprantis C. — An Invitation to Operator Theory (Graduate Studies in Mathematics, V. 50) :: Электронная библиотека попечительского совета мехмата МГУ

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Abramovich Y., Aliprantis C. — An Invitation to Operator Theory (Graduate Studies in Mathematics, V. 50)

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Название: An Invitation to Operator Theory (Graduate Studies in Mathematics, V. 50)

Авторы: Abramovich Y., Aliprantis C.

Аннотация:

This book offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices using their topological and order structures and properties. Abramovich and Aliprantis give a unique presentation that includes many new and very recent developments in operator theory and also draws together results which are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2002

Количество страниц: 545

Добавлена в каталог: 06.05.2014

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Предметный указатель

$B_{x}$ , band generated by x      20
$C^{\infty}(Q)$ , extended continuous functions      115
$C_{0}(\Omega)$ , functions vanishing at $\infty$       406
$E^{~}$ , order dual of E      21
$E_{x}$ , ideal generated by x      20
$L_{0}(\pi)$       52
$L_{p, 1}$       210
$L_{p, \infty}$       210
$M_{n}(\mathbb{R})$ , space of n x n square matrices      318
$N_{\lambda}$ , eigenspace with eigenvalue $\lambda$       384
$r_{ess}(T)$ , essential spectral radius of T      302
$x_{n}\stackrel{\mathcal{U}}{\rightarrow} x$ , convergence along an ultrafilter      38
$X_{\mathcal{U}}$ , ultrapower of B-space X      40
$\alpha(T)$ , ascent of operator T      80
$\delta(T)$ , descent of operator T      80
$\ell_{1}$ -sum of Banach spaces      472
$\ell_{p}$ -sum of Banach spaces      281
$\ell_{\infty}$ -sum of Banach spaces      472
$\hat{\mathcal{F}}_{red}(X, Y)$ , semi-Fredholm operators      166
$\mathbb{C}$ , complex numbers      2
$\mathbb{N}$ , the natural numbers, {1,2, ..}      2
$\mathbb{Q}$ , the rational numbers      2
$\mathbb{R}$ , the real numbers      2
$\mathbb{Z}$ , the integers      2
$\mathcal{A}$ -invariant subspace      387
$\mathcal{A}_{T}$ , algebra generated by T      387
$\mathcal{A}_{x}$ , the orbit of x under A      387
$\mathcal{C}$ -invariant collection      410
$\mathcal{F}(X, Y)$ , finite-rank operators from X to Y      125
$\mathcal{F}_{red}(X, Y)$ , Fredholm operators      163
$\mathcal{I}(X,Y)$       472
$\mathcal{K}(X, Y)$ , compact operators from X to V      89
$\mathcal{L}(X)$ , bounded operators on X      2
$\mathcal{L}(X, Y)$ , bounded operators from X to Y      2
$\mathcal{L}_{b}(X, Y)$ , order bounded operators from X to Y      15
$\mathcal{L}_{r}(X, Y)$ , regular operators from X to Y      14
$\mathcal{L}_{\kappa}(E, F)$ , regular integral operators from E to F      188
$\mathcal{R}(A)$ , vector sublattice generated by A      233
$\mathcal{U}$ -limit of sequence      38
$\mathcal{W}(X, Y)$ , weakly compact operators from X to Y      89
$\mathfrak{C}(X)$ , the Calkin algebra      299
$\Phi \otimes Y$ , $\Phi$ -finite-rank operators      125
$\Phi$ -integral operators      193 430
$\sigma$ -Dedekind complete Riesz space      16
$\sigma$ -order closed set      18
$\sigma$ -order complete Riesz space      16
$\sigma$ -order continuous function      18
$\sigma(T)$ , spectrum of operator T      238
$\sigma_{a}(T)$ , approximate spectrum of T      249
$\sigma_{c}(T)$ , continuous spectrum of T      249
$\sigma_{ess}(T)$ , essential spectrum of T      299
$\sigma_{p}(T)$ , point spectrum of T      248
$\sigma_{r}(T)$ , residual spectrum of T      248
$\sigma_{w}(T)$ , Weyl spectrum of T      312
$\| D \|$ , norm of set D      410
(B], super left-commutant of B      399
*-convergence      67
A.e. equal functions      52
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
AL-space      94 101
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, $\mathcal{A}x$       387
Algebra, Calkin      299
Algebra, closed      387
Algebra, dual      387
Algebra, generated by set of operators      387
Algebra, non-transitivc      387 440
Algebra, transitive      387
Algebra, unital      3 386 387
Algebraic complement of subspace      169
Algebraic homomorphism      144
Almost essentially disjoint operators      477
Almost integral operator      193 430
AM-compact operator      401
AM-space      94 101
AM-space with unit      94
AM-space, complex      106
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 $L_{0}(\pi)$ or $\pi$       194
Banach function space, rearrangement invariant      223 494
Banach lattice      22
Banach lattice with order continuous norm      84
Banach lattice, AL      94
Banach lattice, AM      94
Banach lattice, complex      105
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 of abstract integral operators      193 430
Band of integral operators      188
Band preserving operator      112
Band projection      21
Band, generated by a set      20
Band, principal      20 118
Band, projection      21
Basic sequence      30
Basic sequence, unconditional      35
Basis      28 436
Basis constant      29
Basis in $L_{p}[0,1]$       36
Basis problem      28
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 $L_{0}$       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, (B]      399
Commutant, super right, [B)      399
Commutator of two operators      398
Compact operator      88 272
Compact-friendly operator      425
Complement of a closed subspace      386
Complement, algebraic of subspace      169
Complemented subspace      134 386 486
Complete measure      66
Completely continuous function      444
Completion, Dedekind      26
Completion, Maeda — Ogasawara — Vulikh      116
Completion, universal      116
Complex AM-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 in measure      53
Convergence of Laurent series      49
Convergence, *      67
Convergence, notions in $L_{0}$       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
d(T), defect of operator T      155
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, Koethe      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      219
Eigenvector      248
Entire function      47
Equation, Daugavet      156
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
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
f(T)      258
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

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