Conway J.B. — A Course in Functional Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Conway J.B. — A Course in Functional Analysis

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Название: A Course in Functional Analysis

Автор: Conway J.B.

Аннотация:

This book is an introductory text in functional analysis, aimed at the graduate student with a firm background in integration and measure theory. Unlike many modern treatments, this book begins with the particular and works its way to the more general, helping the student to develop an intuitive feel for the subject. For example, the author introduces the concept of a Banach space only after having introduced Hilbert spaces, and discussing their properties. The student will also appreciate the large number of examples and exercises which have been included.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 404

Добавлена в каталог: 01.04.2006

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Предметный указатель

$C_{,}$ (X)      67 78 182 192
$c_{0}$       68 78 147 190
$C_{b}$ (X)      67 108 111 119 141 142 144 192
$L^{1}_{\mu}$       78 137
$L^{p}(\mu)$       68 76 92 382
$L^{\infty}(\mu)$       78 138
$M_{\phi}$       28 70 172 279 284 307
$N_{\mu}$       271 275 276 286 333
$\sigma_{ap}(A)$       213
$\sigma_{p}(A)$       45
*-homomorphism      239 253
A-closed      320
A-symmetric      320
Absolutely continuous      385
Absorbing      105
Absorbing, absorbing at a      105
Adjoint      31 171 312
Affine hyperplane      112
Affine manifold      112
Affine map      146 155
Affine subspace      112
Alaoglu's theorem      134
Algebra      191
Algebraically complemented      97
Almost periodic      163
antisymmetric      89
Approximate identity      199 227
Approximate point spectrum      213
Arzela — Ascoli theorem      179
Backward shift      33 214
Balanced set      105
Banach algebra      191
Banach limit      84 86
Banach space      65
Banach — Steinhaus theorem      100
Banach — Stone Theorem      176
Basis      14 16 101
Basis, Hamel      375
Bergman space      5
Bessel's inequality      15
Bijective      376
Bilateral ideal      195
Bilateral shift      277
Borel measure      387
Borel sets      387
Bounded linear functional      12 77
Bounded operator      27 70 310
Bounded sesquilinear form      31
Bounded set      109 110
Bounded transformation      27 70
Boundedly invertible      314
Boundedly mutually absolutely continuous      276 277
Brower's fixed point theorem      153
C(X)      78 104 109 117 137 140 179 190 192
C*-algebra      237
Calkin algebra      353
Cantor set      292
Cauchy — Bunyakowsky — Schwarz Inequality      3
Cauchy's integral formula      204
Cauchy's theorem      204
Cayley transform      325
CBS inequality      3
CHARACTER      232
Clopen set      215
Closable operator      311
Closed convex hull      104
Closed graph theorem      94
Closed half-space      113
Closed linear span      11
Closed operator      311
Closure of an operator      311
Cluster point of a net      378
Cofinal      89
Commutant      283
Commutator Ideal      226
compact function      153
Compact operator      41 177 219 278
Compact-open topology      236
Complementary subspaces      97
completely continuous      177
Completely regular      140 144
Complex measure      384
Complexification      7
Compression spectrum      355
Cone      89
Convergence nets      378
Convergence unconditional      19
Convergence uncountable sums      16
Convex hull      104
Convex set      8 104
Convolution      193 228
Coset      376
Cyclic operator      255
Cyclic representation      255
Cyclic vector      60 255 275
Deficiency indices      319
Deficiency subspaces      319
Densely defined      311
Derivative as a distribution      126
Diagonahzable      30 45 47 55 56 57 273 277
Diagonal operator      30 43 45 55
DIMENSION      17
Direct integral      308
Direct sum of Hilbert spaces      24
Direct sum of normed spaces      74
Direct sum of operators      30
Direct sum of representations      255
Directed set      377
distribution      124
Distribution, derivative of      126
Division algebra      222
Double commutant      283
Double commutant theorem      284
Dual group      232 235
Dual space      77 117
Eberlein — Smulian theorem      167
Eigenspace      213
Eigenvalue      45 213
Eigenvector      45 213
Equicontinuous      179
Equivalent representations      255
Essential range      271 296
Essential spectrum      355
Essential supremum      28
Extension      311
Extreme point      145 281
Final space      248
Finite rank      42 178
Fourier coefficient      22
Fourier expansion      22
Fourier series      22
Fourier transform      22 234 343
Frechet space      109 111
Fredholm alternative      221 361
Fredholm index      361
Fredholm operator      356
Fuglede — Putnam theorem      285 334
Function algebra      150
Functional calculus      58 206 243 295
Functional calculus, for compact normal operators      58
Functional calculus, for normal operators      243 295
Functional calculus, Riesz      206 272
Gauge      106
Gelfand transform      225
Gelfand — Mazur theorem      223
Gelfand — Naimark — Segal construction      257
Generator      225 227
GNS construction      258
Gra A      94 311
Gram — Schmidt orthogonalization process      14 18

Graph      311
Green function      52
Group algebra      229
H(G)      104 118
Haar measure      159
Hahn — Banach theorem      80 111
Hahn — Jordan decomposition      384
Half-space      113
Hamburger moment problem      349
Hamel basis      375
Hermite polynomials      18
Hermitian      33 239
Hilbert matrix      30
Hilbert space      4
Hilbert — Schmidt operator      273 274
Holes of a set      211
Hyperinvariant subspace      185
Hyperplane      76
Ideal      195
Ideal modular      198
Ideal of $\mathcal{B}(\mathcal{H})$       253 278
Idempotent      37 46
Imaginary part of an operator      34
INDEX      218 361
Inductive limit topology      120
Inductive system      119
Infinitesimal generator      340
Inflation      255 263
Initial space      248
Injective      376
Inner product      2
Inside of curve      204
Integral operator      29 43 71 172
Integral with respect to a spectral measure      264
Invariant subspace      39 182
Inverse mapping theorem      94
Inversion formula      347
Invertible      195
Involution      237
Irreducible operator      63
Irreducible representation      268
Isometrically isomorphic      69
Isometry      20 218
Isomorphic      19 96
Isomorphism of Banach spaces      69 96
James's Theorem      168
Jordan decomposition      384
Kernel of an integral operator      29 71
Kernel of an operator      376
Krein — Milman theorem      146
Krein — Smulian Theorem      163 168
L      68 78 139 192
L;(G)      5 359 362
Laguerre polynomials      18
Larger topology      380
Laurent expansion      215
LCS      103
Left essential spectrum      355
Left Fredholm operator      356
Left ideal      195
Left invertible      195
Left modular ideal      198
Left modular unit      198
Left regular representation      238
Left resolvent set      199
Left spectrum      199
Left spectrum, of an operator      200
Legendre polynomials      18
Line segment      104
Linear functional      11 76 111 376
Linear manifold      10 376
Linear operator      310
Linear subspace      10
Linear transformation      26 70 376
Linearly independent      375
Lipschitz function      101
Locally convex space      103
Lomonosov's Lemma      184
Lomonosov's theorem      186
m(X)      78 79 151
Markov — Kakutani Fixed Point Theorem      155
Maximal ideal      197
Maximal ideal space      224
Mazur's theorem      184
Measurable space      384
Measure      384
Measure space      384
Metrizable      109 111 138
Minkowski functional      106
Modular ideal      198 199 227
Modular identify      199
Moments      349
Multiplication formula      347
Multiplication operator      28 46 70 172 279 284
Multiplicity      62 287 299 307
Multiplicity function      62 307
Mutually absolutely continuous      276
Mutually singular      385
Natural map      92
Negative part      246
Net      377
Noncontracting family      157
Norm      4 12 27 66 70
Norm equivalent      66
Norm essential supremum      28
Normable      110
normal      33 239 326
Normal operator      33
Normed space      65
Of Hilbert spaces      19
One-parameter unitary group      336
One-point compactification      69 227
Open half-space      113
Open line segment      145
Open mapping theorem      93
Order unit      89
Ordered by inclusion      377
Ordered by reverse inclusion      377
Ordered vector space      88
Orthogonal      7
Orthogonal difference      38
Orthogonal projection      10 37
Orthonormal subset      14
Outside of curve      204
P-diameter      156
Pairwise orthogonal      55
Parallelogram law      8
Parseval's Identify      17
Partial isometry      248 250
Partition of the identity      55
Partition of unity      143
Plancherel transform      348
Plancherel's Theorem      348
Point spectrum      213
Poisson kernel      199
polar      129
Polar decomposition      61 248 273
Polar identity      4
Polynomially convex      211
Polynomially convex hull      211
Pontryagin Dualify Theorem      234
Positive element in a C*-algebra      246
Positive functional      89 256
Positive linear map      59 89
Positive measure      384
Positive operator      59 89
Positive part      246
Positively oriented      204
Prepolar      129
Principle of uniform boundedness      98 100 130

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