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Abramovich Y.A., Aliprantis C.D. — An Invitation to Operator Theory
Abramovich Y.A., Aliprantis C.D. — An Invitation to Operator Theory



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Название: An Invitation to Operator Theory

Авторы: Abramovich Y.A., Aliprantis C.D.

Аннотация:

Since the appearance of the seminal monograph of Stefan Banach [51] on (linear) operators between normed spaces, the study of operators has been at-the heart of research in analysis. For the most part, this research was confined to the topological structures of the spaces and to the topological properties of the operators. At the same time there was one more aspect of operator theory that was developed in parallel with the topological and algebraic study of operators. This natural aspect involved the order structures of the spaces between which the operators acted.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 544

Добавлена в каталог: 15.07.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$AL$-space      94 101
$AM$-compact operator      401
$AM$-space      94 101
$AM$-space, complex      106
$AM$-space, with unit      94
$B_{x}$, band generated by $x$      20
$C^{\infty}(Q)$, extended continuous functions      115
$C_{0}(\Omega)$, functions vanishing at oo      406
$d(T)$, defect of operator $T$      155
$E^{~}$, order dual of $E$      21
$E_{x}$, ideal generated by $x$      20
$F(T)$      258
$KB$-space      85
$L$-space      122
$L_{0}(\pi)$      52
$l_{1}$-sum of Banach spaces      472
$L_{p, 1}$      210
$L_{p,\infty}$      210
$M$-space      122
$M_{n}(\mathbb{R})$, space of $n\times n$ square matrices      318
$n(T)$, nullity of operator $T$      155
$N_{\lambda}$, eigenspace with eigenvalue $\lambda}$      384
$r$-norm of operator      22
$r_{ess}(T)$, essential spectral radius of $T$      302
$T^{**}$, the double adjoint of operator $T$      4
$T^{*}$, the adjoint of operator $T$      4
$U$, $U^{*}$, $U^{**}$, closed unit balls      3
$X^{**}$, double norm dual of $X$      3
$X^{*}$, norm dual of $X$      3
$x_{n} \overset{\mathcal{U}}{\rightarrow} x$, convergence along an ultrafilter      38
$X_{\mathcal{U}}$, ultrapower of $B$-space $X$      40
$[B\rangle$, super right-commutant of $B$      399
$\alpha(T)$, ascent of operator $T$      80
$\delta(T)$, descent of operator $T$      80
$\hat{F}_{red}(X,Y)$, semi — Fredholm operators      166
$\langle B]$, super left-commutant of $B$      399
$\l_{p}$-sum of Banach spaces      281
$\l_{\infty}$-sum of Banach spaces      472
$\mathbb{C}$, 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 $\mathcal{A}$      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 $Y$      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
$\mathcal{L}_{k}(E, F)$, regular integral operators from $E$ to $F$      188
$\mathcal{L}_{r}(X, Y)$, regular operators from $X$ to $Y$      14
$\mathcal{R}(A)$, 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
$\Phi$-integral operators      193 430
$\Phi\otimes Y$, $\Phi$-finite-rank operators      125
$\sigma$-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
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, $\mathcal{A}_{x}$      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 $L_{0}(\pi)$ or $\pi$      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 $L_{p}[0, 1]$      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 $L_{0}$      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, $\langleB]$      399
Commutant, super right, $[B\rangle$      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 $AM$-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      67
Convergence, $*$      67
Convergence, convergence, of Laurent series      49
Convergence, in measure      53
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
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, K$\ddot{o}$ther      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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