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Eidelman Y., Milman V., Tsolomitis A. — Functional Analysis. An Introduction
Eidelman Y., Milman V., Tsolomitis A. — Functional Analysis. An Introduction

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Название: Functional Analysis. An Introduction

Авторы: Eidelman Y., Milman V., Tsolomitis A.

Аннотация:

The goal of this textbook is to provide an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 322

Добавлена в каталог: 31.03.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Alaoglu      149
Algebra semisimple      181
Algebraic span      185
Almost periodic function      188
Analytic functions      172
Arzell      60
Baire category      128
Baire — Hausdorff      128
Banach algebra      167
Banach limit      163
Banach space      17 127
Banach — Steinhaus      67 135 136
Band matrix      70
Basis      140
Basis of a normed space      31
Basis of space      5
Bessel inequality      29 31
Biorthogonal functionals      139
Biorthogonal system      50
Birkhoff's theorem      155
Bounded functional      38
Bounded set      14
Bounded variation      161
Category      128
Cauchy integral      173
Cauchy sequence      16
Cauchy — Schwartz inequality      10 26
Cayley transform      216
Center of a set      129
Centrally symmetric      14
Closed graph operator      132 133
Closed set      12
Closure      13
Closure of operator      133
Codimension      6
Compact operators      59
Compact set      59
complete      18
Complete space      17
Complete system      29 30
Completion      19 21 117
conjugate      184
Continuous functional      38
Continuous spectrum      76 212
Convex      14 35 144
Convex set      13
Convolution of sequences      169
cosets      5
Decomposition of the identity      109
Dense set      13
Dimension of space      5
Dirac measure      157
Direct decomposition      101
Dirichlet kernel      139
Distance to a set      35
Domain of operator      203
Dual norm      47
Dual operator      63
Dual space      47 51
Eberlain — Schmulian      152
Eigenvalue      75 211
Eigenvalue, multiplicity      76
Eigenvector      212
Embedding operator      60
Equicontinuous      60
Equivalent norms      8
Essential involution      188
Extremal point      153 154
Extremal set      153
Field      171
Finite rank, rank operators      65
Finite support sequence      4
First category set      128
Fisher      93
Fourier transform      121
Fredholm, first theorem      81
Fredholm, second theorem      81
Fredholm, theory      77
Fredholm, third theorem      82
Gelfand      167 171
Gelfand map      176
Gelfand theorem      171
Gelfand — Mazur      176
Gelfand — Naimark theorem      186
Generalized Cauchy — Schwartz inequality      96
Generalized nilpotent      182
Generator of simple spectrum      116
Goldstein      151
Gram-Schmidt      30
Graph method      215
Graph of operator      132
Haar system      162
Hahn — Banach      47 142
Heine — Borel      107
hilbert      3 25
Hilbert space      33
Hilbert — Courant      93
Hilbert — Schmidt, first theorem      90
Hilbert — Schmidt, second theorem      94
Hilbert, space      27 28
Hilbertian norm      27
Holder's inequality      9
Hormander      134
Ideal      170
Image      4
Index of defect      206
Inequality, Cauchy — Schwartz      10 26
Inequality, Cauchy — Schwartz, generalized      96
Inequality, Hoelder      9
Inequality, Hoelder, integral form      10
Inequality, Minkowski      11
Inequality, Minkowski, integral form      12
Inner product      25
Integral representation      173
interval      13
Invariant subspace      87 90
Inverse operator      68
Invertible, element of a Banach algebra      170
Invertible, operator      68
Involution      184
Involution, essential      188
Isometry      19 116
Isometry, into      19
Isomorphism      4
James      153
Kernel      4 15 130
Kernel function      57
Kernel of a set      129
Kernel of an operator      57
Krein — Milman      153 154
Limit along an ultrafilter      193
Linear functional      37
Linear functional, positive      188
Linear map      3
Linear space      3
Linear span      5
Linearly dependent set      5
Linearly dependent vectors      5
Linearly independent      30
Linearly independent relative to subspace      6
Linearly independent vectors      5
Livshic      129
Loranian polynomial      122
Majorizing element      172
Maximal ideal      171
Measure, Dirac      157
Measure, probability      156
Measure, strongly regular      156
Mercer's theorem      95 96
Minimal system      139
Minimax principle      93
Minkowski's functional      146 147
Minkowski's inequality      11
Multiplicity of the eigenvalue      76
Non-separable      41
Norm      7
Norm, convergence      67
Norm, equivalent      8
Norm, stronger      8
Normed space      7 8 14
Normingset      164
Nowhere dense      128
Open ball      12
Open map      69
Open radius      12
Open set      12
Operator      55
Operator of finite rank      65
Operator self-adjoint      87 204
Operator symmetric      87 204
Operator unitary      116
Operator unitary equivalent      117 224
Operator, compact      59
Operator, domain      203
Operator, graph of      132
Operator, index of defect      206
Operator, isometry      116
Order of self-adjoint operators      96
Orthogonal, complement      36
Orthogonal, decomposition      34 35
Orthonormal system      28
Orthoprojection      101
Pairing      64
Parallelogram law      27 88
ParsevaTs identity      32
Perfectly convex set      129
Point spectrum      75
Polya      138
Polydisc      199
Positive linear functional      188
Precompact, set      59
Precompact, space      60
Probability measure      156
Projection      34
Projection operators      100
Projection spectral family      124
Proper ideal      170 171
Pythagorean Theorem      27
Quotient, normed space      14
Quotient, radical      181
Quotient, space      5 19
Ramsey theorem      194
Rank of an operator      65
Reducing subspace      122
Reflexive space      50
Regular point      75 173
Relatively compact set      59
Residual spectrum      76 212
Riesz representation      40
Scalar product      25
Schauder basis      140
Second category      128
Second category set      128
Self-adjoint, element      185
Self-adjoint, operator      87 204
Semilinearity      25
Seminorm      15
Semisimple algebra      181
Separable space      31
Separation of convex sets      147
Set, center of      129
Set, compact      59
Set, first category      128
Set, kernel of      129
Set, perfectly convex      129
Set, precompact      59
Set, relatively compact      59
Shift operator      58
Simple spectrum      116
Simple spectrum, generator      116
Singular point      174
Space, Banach      17 127
Space, of bounded operators, of maximal ideals      176
Space, reflexive      50
Spectral decomposition      108
Spectral, decomposition      108 217
Spectral, family      109
Spectral, family of projections      124
Spectral, integral      110
Spectral, properties      121
Spectral, theory      75
Spectrum      75 211
Spectrum point      75
Strong convergence      67
Stronger norm      8
Strongly, continuous function      161
Strongly, holomorphic function      161
Strongly, regular measure      156
Sublinear function      142
subspace      4
Subspace, invariant      87
Symmetric algebra      185
Symmetric extension      204
Symmetric kernels      94
Symmetric operator      87 204
system      162
Tensor product      66
Theorem Alaoglu      149
Theorem Banach — Steinhaus      136
Theorem Cauchy      173
Theorem Eberlain — Schmulian      152
Theorem Fredholm, first      81
Theorem Fredholm, second      81
Theorem Fredholm, third      82
Theorem Gelfand      171
Theorem Gelfand — Naimark      186
Theorem Goldstein      151
Theorem Hahn — Banach      47 142
Theorem Hormander      134
Theorem James      153
Theorem Krein — Milman      153 154
Theorem Liouville      175
Theorem Mercer      95
Theorem Polya      138
Theorem Ramsey      194
Theorem Wiener      178
Total set      48
Triangle inequality      7
Uniform convergence      67
Uniformly bounded      60
Unit ball      14
Unit sphere      14 48
Unitary operator      121
Unitary operators      116
Unitary operators equivalent      116 224
Volterra operator      82
Weak convergence      68
Weak topology      148
Weakly continuous function      161
Weakly holomorphic function      161
WeierstralS      30
Wiener algebra      169 178
Wiener theorem      178
Zabreiko      135
Zorn's lemma      154
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