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Robertson A.P., Robertson W. — Topological vector spaces
Robertson A.P., Robertson W. — Topological vector spaces

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Название: Topological vector spaces

Авторы: Robertson A.P., Robertson W.

Аннотация:

The aim of tbli tract is to give an account of the theory of topological vector spaces. There are many branches of functional analysis which depend upon this theory; it forms, for example, the background for the theory of distributions. In addition, it often clarinet results in the theory of normed spaces, especially those concerned with the weak topology, to regard them as particular cases of more general results about topological vector spaces. In this tract we have tried to present the main theorems as simply and directly as is possible without sacrificing any of their force or generality. It has been our purpose to make the basic ideas and facts of the subject easily accessible. With this in mind, we have assumed only a minimum of knowledge of general topology and linear algebra to start with; the details of what is assumed are to be found at the beginning of the first chapter. After this, new topological concepts am introduced when they are needed. The first four or five chapters contain the fundamental results; here the pace is leisurely. Some of these could have been deduced more concisely from general topological theorems, but we have preferred to keep the treatment self-contained and establish them directly for topological vector spaces, or even for locally convex spaces. From the sixth chapter onwards the proofs are more condensed; here we have allowed ourselves to be guided to some extent by our own interests in the choice of subject matter.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1964

Количество страниц: 166

Добавлена в каталог: 04.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolutely convex      4
Absorb      44
Absorbent      5
Adjoint mapping      38
Algebraic, conjugate      25
Algebraic, dual      25
Ascent, finite      145
Baire space      73
Balanced      4
Ball, unit      16
Banach space      60
Banach — Steinhaus theorem      65 70
Barrel      65
Barrelled      65
Base      3
Base of neighbourhoods      7
Base, dual      36
Base, filter      56
Bicontinuous      8
Bilinear, form      31 130
Bilinear, mapping      130
Bipolar      35
Bornological      81
Bounded, mapping      81
Bounded, set      44
Bounded, strongly      70
Bounded, weakly      70
Canonical mapping      77
Category, first      73
Category, second      73
Cauchy, filter      58
Cauchy, sequence      60
Chain      3
Closed set      6
Closure      6
Closure, point of      6
Cluster point      109
Coarser (topology)      7
Compact, mapping      143
Compact, set      52
Compatible      9
complete      59
Complete, fully      111
Completion      101
conjugate      25
Conjugate, mapping      38
continuous      8
Convergence, of filter      56
Convergence, of sequence      55
Convex      4
Convex, envelope      5
Convex, space      10
coordinates      87
Covering      52
Covering, open      52
Dense      6
Descent, finite      145
Determined by seminorms (topology)      15
Direct sum      89
Direct sum, topology      90
Distance      7
distribution      41
Dual      25
Dual, algebraic      25
Dual, mapping      38
Dual, pair      32
Dual, reflexive dual pair      72
Dual, topology of dual pair      34
Eberlein's theorem      109
Eigenvalue      142
Eigenvector      142
Envelope, absolutely convex      5
Envelope, convex      5
Equicontinuous      24
Equicontinuous, convergence (topology of)      137
Equivalent metrics      7
Euclidean topology      37
Extremal point      138
Extremities of line segment      138
Filter      56
Filter, base      56
Filter, Cauchy      58
Filter, elementary      57
Filter, generated      56
Finer, (filter)      56
Finer, (topology)      7
Form, bilinear      130
Form, linear      25
Frechet space      60
Fully complete      111
Gauge      13
Graph      114
Graph, closed graph theorem      116 123
Hahn — Banach theorem      26 29
Hausdorff      7
Homeomorphic      8
Homeomorphism      8
Homomorphism      113
Hypercomplete      125
Hyperplane      25
Induced limit      79
Induced limit, strict      127
Induced topology      8
Injection mapping      88
Interior      6
Interior, point      6
Interior, point of line segment      138
Isomorphic      24
Isomorphism      24
Krein — Milman theorem      138
Krein's theorem      128
Line segment      138
Linear, form      25
Linear, functional      25
Linear, mapping      23
Linearly independent      2
Locally convex      10
Mackey, space      81
Mackey, topology      62
Mapping, bilinear      130
Mapping, linear      23
Maximal      3
Measure, Radon      40
Metric      7
Metric space      7
Metrisable      7
Minimal      3
Montel space      74
n-Dimensional      4
Nearly, closed      111
Nearly, continuous      115
Nearly, open      113
Neighbourhood      6
Neighbourhood of origin      9
Nilpotent      148
Norm      13
Normable      16
Nowhere dense      73
Nuclear      141
open      6
Open covering      52
Open mapping      112
Operation      23
Operator      23
Orthogonal      35
polar      34
Polar topology      46
Precompact      49
Product topology      87
Projection mapping      87
Projective, limit      84
Projective, tensor product topology      132
Projector      97
Quotient      76
Quotient, topology      77
Radon measure      40
Rapid decrease      19
Refinement, filter      56
Reflexive, dual pair      72
Reflexive, space      72
Riesz theory      142
Schauder's theorem      153
Seminorm      12
Separated      7
Separately continuous      136
Small of order U      49
Spectrum      142
Strong topology      47
Subspace, vector      2
Supplement, algebraic      96
Supplement, topological      96
Support, of convex set      139
Support, of distribution      41
Support, of function      18
Support, of measure      41
Tensor product      130
Tensor product, topological      132
Topological, space      6
Topological, vector space      9
Topology, direct sum      90
Topology, Mackey      62
Topology, of $\mathscr{A}$-convergence      46 68
Topology, of compact convergence      18
Topology, of compact convergence for all derivatives      19
Topology, of equicontinuous convergence      137
Topology, of uniform convergence      17 46 68
Topology, polar      46
Topology, product      87
Topology, strong      47
Topology, weak      32
Totally bounded      50
Transformation      23
Tychonoff's theorem      64
Ultrafllter      57
Vanishes at infinity      63
Vector subspace      2
Vector subspace, spanned by      2
Weak topology      32
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