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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



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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
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Предметный указатель
Norm of a bounded operator      41 100
Norm of a conjugate-bilinear functional      100
Norm of a direct sum of operators      122
Norm of a Hilbert — Schmidt functional      128
Norm of a linear functional      44
Norm of a matrix with operator entries      151
Norm of a multilinear functional      126
Norm of a multilinear mapping      131
Norm of a tensor product of operators      146
Norm of a weak Hilbert — Schmidt mapping      131
Norm on $l_p$      50 51
Norm on $l_\infty$      49
Norm on a Banach algebra      174
Norm on a C*-algebra      236 237
Norm on a direct sum of Hilbert spaces      121
Norm on a Hilbert space      77
Norm on a normed algebra      174
Norm on a tensor product of Hilbert spaces      132 135
Norm on C(S)      49
Norm topology      35 66
Norm-preserving (linear mapping)      36
Normal element of a C*-algebra      237
Normal function      344 355
Normal operator      see Operator Unbounded
Normal state      376
Normed algebra      174
Normed space      35
Nowhere-dense set      60 322
Null function      52
Null projection (of a linear operator)      118
Null set      52
Null space (of a linear operator)      2 118 171
One-parameter unitary group      282 367
Open mapping      59
Open mapping theorem      61
Operator      see also Unbounded operator
Operator affiliated      342
Operator bounded      41 100
Operator compact      165 166 226 227
Operator compact self-adjoint      166 167
Operator conjugate-linear      15
Operator Hilbert — Schmidt      141
Operator linear      2
Operator normal      103 319 321 322 350 354 357
Operator positive      103
Operator real-linear      15
Operator-monotonic increasing      250 294 295
Order unit      213 249 255 297
Orthogonal      87
Orthogonal complement      88
Orthogonal family of projections      113
Orthogonal set      88
Orthonormal basis      91
Orthonormal set      88
Parallelogram law      80
Parseval’s equation      91 120
Partially ordered vector space      213 249 255 295 296 297
Partially ordered vector space archimedian      297
Plancherel’s theorem      201 231 232
Point spectrum      357 376
Polar decomposition      105 294
Polarization identity      102
Polynomial Hermite      97
Polynomial Jacobi      97
Polynomial Laguerre      97
Polynomial Legendre      97
Positive element of a C*-algebra      244
Positive linear functional on a C*-algebra      255
Positive linear functional on a partially ordered vector space      213 295 296
Positive linear functional on C(X)      213
Positive n-th root      275
Positive operator      see Operator Unbounded
Positive square root      167 248 364
Pre-Hilbert space      79 81
Principle of uniform boundedness      64 65 74
Projection-valued measure      318 321 360
Projections      12 24 109 110
Projections $\sigma$-finite      338
Projections countably decomposable      338 340 380
Projections cyclic      336
Projections orthogonal      109
Projections spectral      362
Projections, intersection of      111
Projections, join of      111
Projections, meet of      111
Projections, orthogonal family of      113
Projections, union of      111
Pure state of a C*-algebra      261 269
Pure state of a partially ordered vector space with order unit      213
Pure state of B(H)      302 303
Pure state of C(X)      213
Pure state space      261
Pure state, extension of      234 266 296
Quotient Banach algebra      177
Quotient Banach space      39
Quotient C*-algebra      300
Quotient linear space      2
Quotient mapping      2 9 42
Quotient norm      39
Quotient normed space      39
R-essential representation      316
Radical      228
Radius of convergence      204
Radon — Nikodym derivative      56
Radon — Nikodym theorem      56
Range (of a linear mapping)      2
Range projection      118 171
Range space      118
Real-linear functional      7
Real-linear operato      15
Real-linear subspace      8
Reduced atomic representation      282
Reflexive (Banach space)      45 47 67 70 73 98
Regular (element of a Banach algebra)      176
Regular Borel measure      53 54
Representation cyclic      276 278 279
Representation essential      282
Representation faithful      275 264
Representation of a * algebra      282
Representation of a C*-algebra      275
Representation reduced atomic      282
Representation universal      281
Representation, direct sum      281
Representation, equivalent      280
Representation, function      263 264
Representation, R-essential      316
Resolution of the identity      311
Resolution of the identity bounded      311 313
Resolution of the identity unbounded      311 316 343 344 345 348 350
Riemann — Lebesgue lemma      197
Riesz decomposition property      214
Riesz representation theorem      53
Riesz’s representation theorem      97
Rodrigues’s formula      97
Self-adjoint algebra of operators      237 282 309
Self-adjoint element of a C*-algebra      237
Self-adjoint function      344
Self-adjoint function representing an operator      348
Self-adjoint operator      103 157 160 310 313 341 345 348
Self-adjoint set      237
Semi-norm      8 10 17 28
Semi-simple      228
Separable Banach space      57 58 73 74
Separable Hilbert space      94
Separable metric space      57
Separable topological space      57
Separating family of linear functionals      28
Separating family of semi-norms      17
Separating set of vectors      336 337
Separating vector      336 338 339 380
Separation of convex sets      4
Separation strict, of convex sets      4
Separation theorems      4 7 20 21
Shift one-sided      186
Shift two-sided      186 227
Simple C*-algebra      377
Simple tensor      135
Singular (element of a Banach algebra)      176 229
Spectral mapping theorem      181 207 241 273
Spectral projection      362
Spectral radius      180 185 205
Spectral radius, formula      202 204
Spectral resolution      310 312 313 360
Spectral resolution of a representation      315 316 367
Spectral theorem algebraic      239 270 310 349
Spectral theorem for a bounded self-adjoint operator      310 313
Spectral theorem for an unbounded self-adjoint operator      345 348
Spectral value      178
Spectrum      178
Spectrum of an unbounded operator      357
Spectrum, point spectrum      357 376
Square root in a Banach algebra      233 234
Square root in a C*-algebra      248
Square root of a positive operator      364
Stable subspace      121
State definite      289 292
State faithful      288
State of a C*-algebra      255
State of a partially ordered vector space with order unit      213
State of C(X)      213
State space      257
State vector      256 281 289 298 302
State, extension of      234 266 296
Stone — Weierstrass theorem      219 221 235
Stone’s theorem      187 282 367 381
Strong-operator continuity (of functions)      327 328 378
Strong-operator topology      113 304 305 380
Sublattice      235
Sublinear functional      8 9 65
Subprojection      110
Subspace closed, generated by a set      22
Subspace complementary      11 63 88
Subspace finite-dimensional      22 23 24
Subspace generated by a set      2
Subspace invariant      121
Subspace linear      1
Subspace real-linear      7
Subspace reducing      121
Subspace stable      121
Summable      25
Support functional      9 65
Support of a measure      219
Support of a positive linear functional on C(X)      219
Tensor product algebraic      139
Tensor product of Hilbert spaces      125 135
Tensor product of operators      145
Tensor product of vectors      135
Tensor, product associativity of      136 146
Tensor, product universal property of      125 135 139
Topological divisor of zero      229
Topology coarser (weaker)      29
Topology induced by semi-norms      17
Topology initial      13
Topology locally convex      16 23
Topology norm      35 66
Topology weak*      31 43 45 46 48 68
Topology weak-operator      304 305 306 371
Topology weaker (coarser)      29
Totally disconnected      222 374
Trace, normalized      289
Transformation linear      see Operator Unbounded
Transformation unitary      104
Transitivity      332
Triangle inequalilty      35
Unbounded operator affiliated      342
Unbounded operator closable (preclosed)      155
Unbounded operator closed      155 357
Unbounded operator densely defined      155
Unbounded operator maximal symmetric      160
Unbounded operator normal      340 350 353 354 360
Unbounded operator positive      357
Unbounded operator preclosed (closable)      155
Unbounded operator symmetric      160
Unbounded operator, adjoint of      157
Unbounded operator, closure of      155
Unbounded operator, core of      155
Unbounded operator, domain of      154 155
Unbounded operator, extension of      155
Unbounded operator, graph of      155
Unbounded operator, products of      157 352
Unbounded operator, spectrum of      357
Unbounded operator, sums of      157 352
Unbounded operator, von Neumann algebra generated by      349 354
Uniform boundedness (principle of)      64 65 74
Uniform structure in a linear topological space      14
Uniform structure in a normed space      35
Uniformly convex      37 161
Union (of projections)      111
Unit ball      36
Unit element      174 236
Unitary element of a C*-algebra      237 242
Unitary exponential      275 286 287 288 313 314
Unitary group      237 286 287
Unitary operator      103 313
Unitary representation      282 367
Unitary transformation      104
Universal representation      281
Unordered sums      25 26 27 28
Vector state      256 281 289 298 302
von Neumann algebra      308
von Neumann algebra generated by an unbounded operator      349 354
W*-topology (weak* topology)      see Topology
Weak topology induced by a family of linear functionals      28 29
Weak topology, the weak topology      30 43 47 66
Weak* topology      see Topology
Weak-operator topology      304 305 306 371
Weierstrass approximation theorem      221
Wiener’s Tauberian theorems      233
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