Abramovich Y.A., Aliprantis C.D. — An Invitation to Operator Theory :: Электронная библиотека попечительского совета мехмата МГУ

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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.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2002

Количество страниц: 544

Добавлена в каталог: 15.07.2013

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Предметный указатель

Strictly singular operator      170
Strictly transitive collection      387
Strong Krein operator      350 371
Strong operator topology      438
Strong unit      20 94 370
Strongly expanding operator      350
Strongly exposed point      490 503
Strongly exposing linear functional      490
Strongly positive matrix      329
Structure space      136
Subalgebra of operators      386
Subgroup of the unit circle      291
Subgroup of the unit circle, dense      291
Sublinear mapping      149
Subnormal operator      453
Subspace invariant under an operator      10
Subspace, -hyperinvariant      348 381
Subspace, complemented      134 386
Subspace, hyperinvariant      348 381
Subspace, invariant      10 348 381
Subspace, lattice      229
Subspace, non-trivial      348 381
Subspace, norming      51
Subspace, positively complemented      230
Subspace, reducing an operator      81 386
Sum of Banach spaces      247 281 472
Sum of Banach spaces, $l_{1}$       472
Sum of Banach spaces, $l_{\infty}$       472
Sum of vector spaces closed      121
Sup norm      64
Super left-commutant      399
Super right-commutant      399
Support of function      58
Support of ideal in $L_{0}$       60
Support point of a set      13
Supporting functional      466
Supremum      15
Surjcctive function      69
Symmetric difference of two sets      66
Symmetric matrix      317
Symmetric operator      465
System, Haar      36
System, Schauder      36
Tensor-product notation      124
Tonelli’s Theorem      63
Topological space, extremally disconnected      96
Topological space, Stonean      96 115
Topology of uniform convergence on compact sets      126
Topology, euclidean      321
Topology, order continuous      84
Topology, strong operator      438
Trace      133 318
Trace, of finite-rank operator      133
Trace, of matrix      318

Transitive algebra      387
Transitive collection      387
Transitive family of operators      410
Transitivity property      14
Transpose of matrix      317
Triangle inequality      2
Trivial center      116
Twist of a set      207
Ultrafilter      37
Ultrafilter, fixed      38
Ultrafilter, free      38
Ultrapower of -space      40
Unbounded component of $\rho(T)$       256
Unbounded operator      2
Unconditional basic sequence      35
Unconditional basis      32 500
Unconditional constant      33
Unconditionally convergent series      31
Uniform boundedness principle      4
Uniform convergence      53
Uniformly convex -space      465
Uniformly convex Banach space      12 457
Uniformly convex norm      12
Uniformly rotund Banach space      457
Uniformly smooth Banach space      457
UNIT      3 20 94 370
Unit, order      20 94
Unit, weak      21 135 350
Unital algebra      3 386 387
Unitary matrix      317
Universal completion      116
Upper triangularizable matrix      326
Upper triangularizing      326
Vector lattice      15
Vector space order      14
Vector space, majorizing      96
Vector space, ordered      14
Vector space, partially ordered      14
Vector space, quotient      8
Vector sublattice      84
Vector sublattice generated by a set      233
Vector, cyclic      328 383
Vector, discrete      86
Vector, strictly positive      135 316
Volterra collection      451
Volterra operator      275
Weak convergence      3
Weak unit      21 135 350
Weak convergence      3
Weakly analytic function      47
Weakly compact operator      89
Weakly expanding operator      350
Weakly unconditionally Cauchy series      480 486
West decomposition      312
Weyl spectrum of operator      312

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