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Kadison R.V., Ringrose J.R. — Fundamentals of the Theory of Operator Algebras (vol. 2) Advanced Theory
Kadison R.V., Ringrose J.R. — Fundamentals of the Theory of Operator Algebras (vol. 2) Advanced Theory



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Название: Fundamentals of the Theory of Operator Algebras (vol. 2) Advanced Theory

Авторы: Kadison R.V., Ringrose J.R.

Аннотация:

This work and Fundamentals of the Theory of Operator Algebras. Volume I, Elementary Theory present an introduction to functional analysis and the initial fundamentals of C* - and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Major concepts are sometimes presented from several points of view; the account is leisurely when brevity would compromise clarity. An unusual feature in a text at this level is the extent to which it is self-contained; for example, it introduces all the elementary functional analysis needed. The emphasis is on teaching. Well supplied with exercises, the text assumes only basic measure theory and topology. The book presents the possibility for the design of numerous courses aimed at different audiences.


Язык: en

Рубрика: Математика/Анализ/Учебники по элементарному анализу/Задачники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 693

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Norm on $\mathrm{L}_\infty$      52
Norm on $\mathscr{N}_p$      545
Norm on a Banach algebra      174
Norm on a C*-algebra      236 237
Norm on a direct sum of Hilbert spaces      121 123
Norm on a direct sum of operators      122 124
Norm on a Hilbert space      77
Norm on a normed algebra      174
Norm on a quotient normed space      39
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 factorization (of a state)      874
Normal function      344 355
Normal operator, bounded      103 319 321 322 688 689
Normal operator, unbounded      340 350 353 354 357 360
Normal product state      818
Normal representation      464
Normal state      376 454 458 462 467 473 492 498 616 623
Normal von Neumann algebra      930 1046
Normed algebra      174
Normed space      35
Nowhere-dense set      60 322
Nuclear C*-algebra      800 858—863 880
Null function      52
Null ideal      672
Null ideal of a representation      672 676 680
Null ideal of separable type      672
Null ideal sequence      585 672 673 685
Null ideal sequence of a bounded normal operator      689
Null ideal sequence of a representation      672 683 685
Null ideal sequence of separable type      672
Null projection (of a linear operator)      118
Null set      52
Null space (of a linear operator)      2 118 171
One-parameter automorphism group      591 607 610 611 616 640
One-parameter subgroup (of a topological, group)      789
One-parameter unitary group      282 367 596
Open mapping      59
Open mapping theorem      61
Operator      see also “Unbounded operator”
Operator, affiliated      342 344
Operator, bounded      41 100
Operator, compact      see “Compact linear operator”
Operator, compact self-adjoint      166 167
Operator, conjugate-linear      15 65 593
Operator, linear      2
Operator, positive      103
Operator, real-linear      15
Operator, trace-class      462 543
Operator-monotonic increasing function      250 294 295
Order unit      213 249 255 297
Orthogonal      87
Orthogonal complement      88
Orthogonal family of projections      113
Orthogonal projection      109
Orthogonal set      88
Orthogonalization process      94
Orthonormal basis      91
Orthonormal set      88
Parallelogram law      80 81
Parseval's equation      91 120
Partial isometry      400 473 474
Partial isometry, final projection of      400
Partial isometry, final space of      400
Partial isometry, initial projection of      400
Partial isometry, initial space of      400
Partially ordered vector space      213 249 255 295 296 297
Partially ordered vector space, archimedean      297
Pauli spin matrices      795
Plancherel's Theorem      201 231 232
Point spectrum      357 376
Polar decomposition for bounded operators      105 399 401 402
Polar decomposition for conjugate-linear operators      594
Polar decomposition for elements of a C*-algebra      294
Polar decomposition for linear functionals      474
Polar decomposition for tensor products of operators      841
Polar decomposition for unbounded operators      404
Polarization identity      102
Polish space (csm space)      1017
Polynomials, Hermite      97
Polynomials, Jacobi      97
Polynomials, Laguerre      97
Polynomials, 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 linear mapping      511 770
Positive linear mapping, completely      881—885
Positive nth root      275
Positive operator      103 357 840
Positive square root      167 248 364
Pre-Hilbert space      79 81
Predual (of a von Neumann algebra)      481 712
Predual (of a von Neumann algebra) of a tensor product      818
Primary representation      see “Factor representation”
Primary state      see “Factor state”
Primitive ideal      791
Primitive ideal space      792 793
Primitive spectrum      792
Principle of uniform boundedness      64 65 74
Product state      803 847 848 853 857 870 877 889 904
Product state of a uniformly matricial algebra      877 904
Product state of the CAR algebra      see “CAR algebra”
Product state, infinite      870 877 904
Product state, normal      818
Product state, pure      848 870
Product state, tracial      848 870
Projection      12 24 109 110;
Projection (in a von Neumann algebra), $\sigma$-finite      338
Projection (in a von Neumann algebra), abelian      419 420 446 447 588
Projection (in a von Neumann algebra), comparison of      399 402 471
Projection (in a von Neumann algebra), countably decomposable      338 340 380 414 492
Projection (in a von Neumann algebra), cyclic      336 471 478 479 492
Projection (in a von Neumann algebra), equivalence of      399 402 471 736
Projection (in a von Neumann algebra), finite      399 411 414 447 588 832
Projection (in a von Neumann algebra), infinite      399 411 588
Projection (in a von Neumann algebra), minimal      411 419 420 424
Projection (in a von Neumann algebra), monic      510
Projection (in a von Neumann algebra), properly infinite      411 412—414 447 588
Projection (in a von Neumann algebra), rational      922
Projection (in a von Neumann algebra), stronger      406 471
Projection (in a von Neumann algebra), weaker      406 471
Projection, intersection of      111
Projection, join of      111
Projection, meet of      111
Projection, orthogonal      109
Projection, orthogonal family of      113
Projection, spectral      362
Projection, union of      111
Projection-valued measure      318 321 360
Pure state of $\mathscr{B}(\mathscr{H})$      302 303 783
Pure state of a C*-algebra      261 269 728 730 731 733 740 750 781 782 848 870
Pure state of a partially ordered vector space with order unit      213
Pure state space      261 782 783 784
Pure state, extension of      234 266 296
Pure state, of C(X)      213
Pure state, tensor product of      848 870
Quasi-equivalence      711 720 735 736 737 740 741 742 743 780 781 905 917
Quasi-subequivalence      780 781
Quotient Banach algebra      177
Quotient C*-algebra      300 715
Quotient linear space      2
Quotient mapping      2 39 42
Quotient norm      39
Quotient normed space      39
Quotient space      39
Radical      228
Radius of convergence      204
Radon — Nikodym derivative      56
Radon — Nikodym theorem      56
Radon — Nikodym theorem, linear      480 601
Radon — Nikodym theorem, Sakai — Radon — Nikodym theorem      473 477
Range (of a linear mapping)      2
Range projection      118 171
Range space      118
Rational operator      922
Rational projection      922
Real-linear functional      7
Real-linear operator      15
Real-linear subspace      7
Reduced atomic representation      282 711 740 741 744 745 746 754 784
Reflection sequence      631
Reflection sequence of vectors      634
Reflection sequence, weak      631
Reflections (about a vector)      631
Reflexive Banach space      45 47 67 70 73 98 772
Regular Borel measure      53 54
Regular element (of a Banach algebra)      176
Relative commutant      876
Relative invariance      976 983
Representation of a * algebra      282
Representation of a C*-algebra      275 281
Representation, $\mathbb{R}$-essential      316
Representation, commuting pair of      852
Representation, cyclic      276 278 279 735
Representation, decomposable      1007 1008
Representation, diagonalizable      1008
Representation, direct sum      281 734 738
Representation, disjoint      711 720 734—743 780 781
Representation, equivalent      see “Unitary equivalence”
Representation, essential      282
Representation, factor      741 742 743
Representation, faithful      275 281
Representation, function      263 264
Representation, normal      464
Representation, primary      see “Representation factor”
Representation, quasi-equivalent      see “Quasi-equivalence”
Representation, quasi-subequivalent      780 781
Representation, universal normal      458 459
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 — Lebesque lemma      197
Riesz decomposition property      214
Riesz representation theorem      53
Riesz's representation theorem      97
Rodrigues's formula      97
Russo — Dye theorem      768
Sakai — Radon — Nikodym theorem      473 477
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      103 157 160 310 313 341 345 348 840
Self-adjoint set      237
Self-dual cone      705 710
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      336 338 339 380 584 590 591 689
Separation of convex sets      4
Separation of convex sets, strict      4
Separation theorems      4 7 20 21
Shift, one-sided      186
Shift, two-sided      186 227
Simple C*-algebra      377 442 756 759 762 763 784 790 865 878 879 921
Simple C*-algebra, derivation of      790
Simple tensor      135
Singular element (of a Banach algebra)      176 229
Singular functional      723 724 725 750 772 782
Spatial theory (of von Neumann algebras)      585
Spectral mapping theorem      181 207 241 273
Spectral multiplicity      670—689
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 for a bounded self-adjoint operator      310 313
Spectral theorem for an unbounded self-adjoint operator      345 348
Spectral theorem, algebraic      239 270 310 349
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      213 255
State of a C*-algebra      255 739
State of a partially ordered vector space with order unit      213
State of C(X)      213
State of product type a      see “CAR algebra”
State of the CAR algebra      see “CAR algebra”
State of type $\mathrm{I}_\mathrm{n}$, $\mathrm{II}_1$, $\mathrm{II}_\infty$, III      780
State space      257
State space, vector      782
State, algebraically equivalent      909
State, automorphic      906 907 909
State, center state      512 582
State, completely additive      454
State, decomposable      1008
State, definite      289 292
State, extension of      234 266 296
State, faithful      288 616 623 772
State, n-state      884 885
State, normal product      818
State, primary      see “Factor state”
State, product      see “Product state”
Stone — Weierstrass theorem      219 221 235
Stone's theorem      187 282 367 381 612 657 658
Strong topology on $i(\mathscr{R}_\sharp)$      995
Strong-operator * topology      1044
Strong-operator continuity (of functions)      327 328 378
Strong-operator topology      113 304 305 329 380 456
Sublattice      235
Sublinear functional      8 9 65
Subprojection      110
Subrepresentation      734 735 736 737
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      2
Subspace, real-linear      7
Subspace, reducing      121
Subspace, stable      121
Summable      25
Support functional      9 65
Support of a measure      219
Support of a normal state      454 468
Support of a positive linear functional on C(X)      219
Tensor product      see also “Product state”
Tensor product of * homomorphisms      805 807 819
Tensor product of * isomorphisms      805 820
Tensor product of abstract C*-algebras      800 846—863
Tensor product of bounded operators      145
Tensor product of factors      829
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