Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Kadison R.V., Ringrose J.R. — Fundamentals of the theory of operator algebras (vol. 1) Elementary Theory
Kadison R.V., Ringrose J.R. — Fundamentals of the theory of operator algebras (vol. 1) Elementary Theory

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Fundamentals of the theory of operator algebras (vol. 1) Elementary Theory

Авторы: Kadison R.V., Ringrose J.R.

Аннотация:

These volumes deal with a subject, introduced half a century ago, that
has become increasingly important and popular in recent years. While they cover the fundamental aspects of this subject, they make no attempt to be encyclopaedic. Their primary goal is to teach the subject and lead the reader to the point where the vast recent research literature, both in the subject proper and in its many applications, becomes accessible.
Although we have put major emphasis on making the material presented clear and understandable, the subject is not easy; no account, however lucid, can make it so. If it is possible to browse in this subject and acquire a significant amount of information, we hope that these volumes present that opportunity—but they have been written primarily for the reader, either starting at the beginning or with enough preparation to enter at some intermediate stage, who works through the text systematically. The study of this material is best approached with equal measures of patience and persistence.


Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1983

Количество страниц: 417

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$l_2$-independent      379
$\beta$-compactification      224
$\sigma$-finite projection      338
$\sigma$-finite von Neumann algebra      338
$\sigma$-ideal      375
$\sigma$-normal homomorphism      321 322 323 324 325 359 360 362 364
$\sigma$-normal mapping      320
*Homomorphism      237
*Isomorphism      237
*Subalgebra      237
Adjoint Banach      48
Adjoint Hilbert      102
Adjoint in an algebra with involution      237
Adjoint of an unbounded operator      157
Affiliated operator      342 344
Algebra $L_1$      187 233
Algebra $L_\infty$      237
Algebra *      237
Algebra abelian (commutative) Banach      180
Algebra abelian C*      210 269
Algebra abelian von Neumann      310
Algebra C*      236
Algebra countably decomposable (von Neumann)      338 339 380
Algebra division      180
Algebra finite-dimensional C*      288
Algebra maximal abelian      308
Algebra normed      174
Algebra of bounded operators      102 186 236 298 299 303 309
Algebra of continuous functions      175 210
Algebra of unbounded continuous functions      355
Algebra of unbounded operators      352 355
Algebra self-adjoint      237 282 309
Algebra simple C*      377
Algebra von Neumann      308
Algebra, Banach      41 174
Algebra, multiplication      308 314 340 343 376 380
Algebra, operator      173 304
Algebra, quotient      177 300
Approximate eigenvector      178 179 183
Approximate identity in $L_1(R)$      191
Approximate identity in C*-algebras      254 293
Approximate identity, increasing, right      254
Approximation theorems Stone — Weierstrass      219 221 235
Approximation theorems, double commutant      326
Approximation theorems, Kaplansky density      329
Archimedian      297
Baire category theorem      60 223
Balanced neighborhood of 0      13
Balanced set      8
Banach algebra      41 174
Banach dual space      44
Banach inversion theorem      61
Banach lattice      297
Banach module      302
Banach space      36
Banach — Orlicz theorem      73
Bessel’s inequality      90 120
Borel measure, regular      53 54
Bound of a linear functional      44
Bound of a linear operator      40
Bounded linear functional      44
Bounded linear operator      41
Bounded multilinear functional      126
Bounded multilinear mapping      131
Bounded set (in a normed space)      36
Boundedly complete lattice      see Lattice
Bounding projection      351
Bounding sequence      351
C*-algebra      236
C*-algebra simple      377
Cauchy criterion      26
Cauchy — Schwarz inequality      77 215 256
Cayley transform      327 328
Central carrier      332 333
Character of $T_1$      231
Character of R      192 282
Character of Z      230
Clopen set      222
Closed graph theorem      62
Closure (of an operator)      155
Codimension      2
Commutant      325
Commutation relations      181
Commutator      181
Compact linear operator      165 166 227
Compact self-adjoint operator      166 167
Compact support      201
Complementary subspaces      11 63 88
Complete (linear topological space)      14
Completion of a normed algebra      174
Completion of a normed space      38
Completion of a pre-Hilbert space      80
Complexification of a real Hilbert space      76 161
Complexification of a real linear space      66
Complexification of a real normed space      66
Compression      121 276
Cone      212 245
Conjugate Hilbert space      131
Conjugate-bilinear functional      100
Conjugate-bilinear functional bounded      100
Conjugate-bilinear functional positive      103
Conjugate-bilinear functional symmetric      103
Conjugate-linear operator      15 65
Convergence of nets in a locally convex space      25
Convergence of series in a normed space      38
Convergence of sums in a locally convex space      25
Convex combination (finite)      3
Convex hull (of a set)      4
Convex hull closed      31
Convex set      3
Convolution      187 230 231
Core (for an unbounded operator)      155 349
Countably decomposable projection      338 340 380
Countably decomposable von Neumann algebra      338 339 380
Cyclic projection      336
Cyclic representation      276 278 279
Cyclic vector      276
Definite inner product      76
Definite state      289
Derivation      301 302
Dimension (of a Hilbert space)      93
Direct sum of Hilbert spaces      121 123
Direct sum of operators      122 124
Direct sum of representations      281
Direct sum of von Neumann algebras      336
Division algebra      180
Double commutant theorem      326
Dual group of $T_1$      231
Dual group of R      192
Dual group of Z      230
Dual space algebraic      2
Dual space Banach      44
Dual space continuous      30 43
Dual space second      43 45
Eigenvalue      109
Eigenvector      108
Eigenvector approximate      178 179 183
Equivalence of function representations      263
Equivalence of representations      280
Essential range of a measurable function      380
Essential range of an $L_\infty$ function      185
Essential representation      282
Essential supremum      52
Essentially bounded      52
Evaluation functional      211
Extension by continuity      14 15
Extension of pure states      266 296
Extension of states      266 296
Extension theorems      see Hahn — Banach theorems
Extreme point      31 32 33 34 163 164 373
Extremely disconnected space      222 223 224 310 322 324 344 349 373 374 375 376
Face      32
Factor      308
Factorization      2 42
Factors through      2 42
Faithful representation      275 281
Faithful state      288
Finite diagonal block (of a matrix)      154
Finite-dimensional space      22 23 24
Finite-dimensional subspace      22 23 24
First category (set of)      322
Fourier coefficients      95
Fourier series      95
Fourier transform      187 197 368
Fourier transform for $L_2$ functions      201
Fourier transform inversion of      198 199
Function calculus Borel (for bounded normal operators)      319 321 322 324 377
Function calculus Borel (for unbounded normal operators)      340 360 361 363 364 366 380
Function calculus continuous      239 240 271 272 273 274 340
Function calculus holomorphic      206
Function calculus uniqueness      273 322 362
Function representation      263 264
Function representation equivalence of      263
Function representation of a Banach lattice      297
Function representation of an abelian C*-algebra      270
Function representation separating      263
Functional conjugate-bilinear      100
Functional linear      2
Functional real-linear      7
Functional sublinear      8 9
Functional support      9 65
Gelfand — Neumark theorem      275 281
Generalized nilpotent      205 225 226 227
Generating set of vectors      336 337
Generating vector for a cyclic projection      336
Generating vector for a representation      276
Generating vector for a von Neumann algebra      336 338 379 380
GNS construction      279
GNS construction (essential) uniqueness of      279
Gram — Schmidt orthogonalization process      94
Graph (of an operator)      62 155
Hahn — Banach theorems, extension type      7 9 10 21 22 44
Hahn — Banach theorems, separation type      4 7 20 21
Hahn — Jordan decomposition      219 258 259 265 290
Half-space (closed or open)      4
Hermite polynomials      97
Hermitian linear functional on a C*-algebra      255
Hermitian linear functional on C(X)      215
Hilbert space      79
Hilbert space conjugate      131
Hilbert space, isomorphism      93 103 104
Hilbert space, pre-Hilbert space      79 80 81
Hilbert — Schmidt functional      127
Hilbert — Schmidt mapping (weak)      131
Hilbert — Schmidt operator      141
Hoelder’s inequality      71 188
Holomorphic function (Banach-space valued)      203
Holomorphic function calculus      206
Hull closed convex      31
Hull convex      4
Hull of a set      211
Hyperplane      4
Ideal in $L_1(R)$ and related algebras      187 190
Ideal in a Banach algebra      177
Ideal in a C*-algebra      251 252 254 277 300 301
Ideal in C(X)      210
Ideal maximal      177 180 210
Idempotent      11 208
Initial topology      13
Inner product      75 76 79
Inner product definite      76 79 277
Inner product positive definite      76
Inner product space      76
Internal point      4
Intersection (of projections)      111
Invariant mean      224
Invariant subspace      121
Invariant subspace in $L_1$ under translations      233
Invariant subspace in Hilbert space      121
Inverse (in a Banach algebra)      176
Inversion theorem Banach      61
Inversion theorem for Fourier transforms      199
Invertible element (in a Banach algebra)      176
Involution      236
Irreducibility algebraic      330 332
Irreducibility topological      330 331 332
Isometric isomorphism      36
Isometric isomorphism natural, from $\mathfrak{X}$ into $\mathfrak{X}^{\#\#}$      45
Isometric isomorphism of C*-algebras      242
Isometric isomorphism of function calculus      240
Jacobi polynomials      97
Kaplansky density theorem      329
Kernel left, of a state      278
Kernel of a representation      276
Kernel of an ideal in C(X)      211
Krein — Milman theorem      32
Laguerre polynomials      97
Lattice      214 215 298
Lattice Banach      297
Lattice boundedly complete      222 223 374 375 376
Lattice, sublattice      235
Legendre polynomials      97
Linear combination (finite)      1
Linear dependence      1
Linear functional      2
Linear functional bounded      44
Linear functional weak* continuous      31
Linear functional weakly continuous      29 30
Linear independence      1
Linear operator      see Operator Unbounded
Linear order isomorphism      214
Linear topological space      12
Linear transformation      see Operator Unbounded
Locally compact (locally convex space)      24
Locally convex space      16
Locally convex space finite-dimensional      23 24
Locally convex space locally compact      24
Locally convex topology      16
Locally finite group      224
Matrix with operator entries      148
Matrix with scalar entries      147
Maximal abelian algebra      308
Maximal ideal      177 180 187 190 210
Meager set      322 375
Minimal projection      309
Minkowski’s inequality for integrals      53
Minkowski’s inequality for sums      50
Multilinear functional      180 183
Multilinear mapping      131
Multiplication algebra      308 314 340 343 376 380
Multiplication operator      106 107 108 109 117 185 315 341 342 343 344
Multiplicative linear functional      180 183 187 269
Multiplicative linear functional on $l_1 (Z)$      231
Multiplicative linear functional on $L_1(R)$      193
Multiplicative linear functional on $L_1(T_1, m)$      232
Multiplicative linear functional on $l_\infty(Z)$      224
Multiplicative linear functional on C(X)      211 213
Multiplicity (of an eigenvalue)      167 227
Natural image of $\mathfrak{X}$ in $\mathfrak{X}^{\#\#}$      45
Neighborhoods balanced      13 18
Neighborhoods in a linear topological space      13
Neighborhoods in a locally convex space      17 18
Neighborhoods in a normed space      35
Neighborhoods in a weak topology      28
Neighborhoods in the strong-operator topology      113
Neighborhoods in the weak* topology      31
Neighborhoods in the weak-operator topology      305
Nilpotent      205
Non-singular (element of a Banach algebra)      176
Norm      8 35
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте