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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
$l_2$-independent      379
$\beta$-compactification      224
$\mathbb{R}$-essential representation      316
$\sigma$-finite projection      338
$\sigma$-finite von Neumann algebra      338
$\sigma$-ideal      375 672
$\sigma$-normal homomorphism      321 322 323 324 325 359 360 362 364
$\sigma$-normal mapping      320
* Automorphism (of a C*-algebra)      546 766 772 785 788 789
* Automorphism (of a C*-algebra), acting freely      926
* Automorphism (of a C*-algebra), inner      624 664 665 785 789 926 927 955
* Automorphism (of a C*-algebra), outer      451 624 928 931 1045 1046
* Automorphism (of a C*-algebra), universally weakly inner      785 789
* Automorphism group (of a C*-algebra)      789
* Homomorphism      237
* Isomorphism      237
* Subalgebra      237
Action (of a group on a measure space), ergodic      554 559 765 766
Action (of a group on a measure space), free      553
Action (of a group on a von Neumann algebra), ergodic      546 547 559
Action (of a group on a von Neumann algebra), free      546
Adjoint in an algebra with involution      237
Adjoint of a conjugate linear operator      594
Adjoint of an unbounded operator      157
Adjoint, Banach      48
Adjoint, Hilbert      102
Affiliated operator      342 344
Algebra of bounded operators      102 186 236 298 299 303 309 755—759
Algebra of compact operators      see “Compact linear operator”
Algebra of continuous functions      175 210
Algebra of unbounded continuous functions      355
Algebra of unbounded operators      352 355
Algebra, $\mathrm{L}_1$      187 233
Algebra, $\mathrm{L}_\infty$      237
Algebra, *      237
Algebra, abelian (commutative) Banach      180
Algebra, abelian C*      see “C*-algebra”
Algebra, abelian von Neumann      see “von Neumann algebra”
Algebra, Banach      41 174
Algebra, C*      see “C*-algebra”
Algebra, Calkin      755—759
Algebra, CAR (Fermion)      see “CAR algebra”
Algebra, countably decomposable (von Neumann)      338 339 380 449
Algebra, division      180
Algebra, finite-dimensional C*      288 432
Algebra, Hilbert      643
Algebra, normed      174
Algebra, nuclear C*      see “C*-algebra”
Algebra, operator      173 304
Algebra, quotient      177 300 715
Algebra, self-adjoint      237 282 309
Algebra, UHF      see “Uniformly matricial algebra”
Algebra, W*      498 794
Algebraic theory (of von Neumann algebras)      585
Algebraically equivalent states      909
Amenable group      933
Analytic set      1000 1017 1031 1037 1040
Annihilators      934
Anti-isomorphism      472 584 591 777 881
Approximate eigenvectors      178 179 183
Approximate identity in $\mathrm{L}_1(\mathbb{R})$      191
Approximate identity in C*-algebras      254 293 768 769
Approximate identity, increasing, right      254
Approximate identity, quasi-central      769
Approximation theorems, Dixmier      504 523
Approximation theorems, double commutant      326
Approximation theorems, Kaplansky density      329
Approximation theorems, Stone — Weierstrass      219 221 235
Approximation theorems, Weierstrass      221
Archimedian (partially ordered vector space)      297
Automorphic representation of $\mathbb{R}$ on a factor      1043 1044
Automorphic representation of a group      937
Automorphic representation, continuous      957 1043—1045
Automorphic representation, unitarily implemented      937 957 1044 1045
Automorphic states      906 907 909
Baire category theorem      60 323
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      302 771 773
Banach space      36
Banach — Orlicz theorem      73
Bessel's inequality      90 120
Bidual (of a C*-algebra)      726 773
Borel function calculus      see “Function calculus”
Borel mapping      1031 1032
Borel measure space      1031 1040
Borel measure space, regular      1031
Borel measure, regular      53 54
Borel structure      1000 1031
Borel structure, Borel sets of      1031 1040
Borel structure, generated by a family of sets      1031
Borel structure, topological      1031 1040
Bound of a linear functional      44
Bound of a linear operator      40
Bounded linear functional      44
Bounded linear operator      see “Operator”
Bounded multilinear functional      126
Bounded multilinear mapping      131
Bounded set (in a normed space)      36
Bounded weak-operator topology      995
Boundedly complete lattice      see “Lattice”
Bounding projection      351
Bounding sequence      351
Bridging lemma      633
C*-algebra      236
C*-algebra, abelian      210 269—275 291 298 670—689 701 702 744—747 782
C*-algebra, finite-dimensional      288 432
C*-algebra, nuclear      800 858—863 880
C*-algebra, singly generated      701
C*-algebra, type I      880
C*-algebra, UHF      see “Uniformly matricial algebra”
C*-algebra, uniformly matricial      see “Uniformly matricial algebra”
C*-norm      850—858
C*-norm, largest      852
C*-norm, smallest      853 858
C*-norm, spatial      851
C*-semi-norm      851
C*-semi-norm, largest      852
Calkin algebra      755—759
Canonical anti-commutation relations      see “CAR”
Canonical image (of $\mathfrak{U}_a$ in $\otimes\mathfrak{U}_a$)      866
CAR      759 795 796 904
CAR algebra      759 763—766 794 796 889 904 910 914 917 920 955 992
CAR algebra, factor representations of      914 920 955 992—993
CAR algebra, irreducible representations of      763—766
CAR algebra, product states of      889 904 955 992—993
CAR algebra, quasi-equivalent representations of      917
CAR algebra, states of product type a of      910 914 917 920
CAR, irreducible representation of      796 935
CAR, representation of      796 934 935
Carrier (of a state)      454 468
Cauchy criterion      26
Cauchy — Schwarz inequality      77 215 256 489
Cayley transform      327 328 930
Center state      512 582
Center-valued trace      see “Trace”
Central carrier      332 333 403 736
Central decomposition      1028
Centralizer (of a state)      617
Character of $\mathbb{R}$      192 282
Character of $\mathbb{T}_1$      231
Character of $\mathbb{Z}$      230
Character of a locally compact abelian group      1041
Clopen set      222
Closed graph theorem      62
Closure (of an operator)      155
Codimension      2
Commutant      325 584
Commutant of a tensor product      800 812 821 828 843
Commutant, type of      585—590
Commutation relations      181
Commutation theorem      812 821 828 843
Commutator      181
Compact linear operator      165 166 226 227 747—755 782 783
Compact linear operator, algebra of      747—755 782 783
Compact self-adjoint operator      166 167
Compact support      201
Comparison of projections      399 402 471
Comparison of projections in a factor      408
Comparison theorem      408 409
Comparison theory      399—422 471
Complementary subspaces      11 63 88
Complete (linear topological space)      14
Complete (measure space)      1031
Completely positive linear mapping      881—885
Completion of a measure space      1031
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
Conditional expectation      571 572 573 794 834 836
Conditional expectation, faithful      572
Cone      212 245
Cone, dual      704 705
Cone, self-dual      705 710
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 65 593
Continuous crossed product      see “Crossed product”
Continuous function calculus      see “Function calculus”
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 (of a set), closed      31
Convex set      3
Convolution      187 230 231 433 1041
Core (of an unbounded operator)      155 349
Core (of an unbounded operator) of a tensor product of operators      838
Countably decomposable projection      338 340 380 413 414 492
Countably decomposable von Neumann algebra      338 339 380 449
Coupling (or Linking) constant      690
Coupling (or Linking) operator      691 698
Creator      934
Cross-norm      851 858
Crossed product      936—997
Crossed product by a modular group      936 974
Crossed product of factors      941 948
Crossed product, abstract continuous      966
Crossed product, abstract discrete      938
Crossed product, continuous      936 957—974
Crossed product, discrete      936 937—956
Crossed product, duality for      936 970
Crossed product, implemented continuous      968
Crossed product, implemented discrete      939
Crossed product, second      936 957 968 970
Csm space      1017 1020 1036 1040
Cyclic projection      336 471 478 479 492
Cyclic projection, comparison of      471
Cyclic representation      276 278 279 735
Cyclic vector      276
Dauns — Hoffman theorem      793
Decomposable operator      999 1002
Decomposable operator, algebra of      1005 1027
Decomposable representation      1007 1008
Decomposable state      1008
Decomposable von Neumann algebra      999 1009 1010 1011
Decomposition      see “Direct integral decompositions”
Definite inner product      76
Definite state      289
Density matrix      462
Derivation      301 302 492 580 581 582 771 784 785 788 790 791
Derivation of a simple C*-algebra      790
Derivation of a von Neumann algebra      582
Derivation, * derivation      784 785 788 790
Derivation, inner      580 582 790
Diagonalizable operator      999 1002
Diagonalizable operator, algebra of      1005 1027
Diagonalizable projection      1003
Diagonalizable representation      1008
Diagonalization (of a representation)      1008
Dimension function      504 529 530—537
Dimension of a Hilbert space      93
Dimension, generalized in variance of      416
Direct integral decompositions      998 999 1025—1031
Direct integral decompositions and type decomposition      1015 1028
Direct integral decompositions into factors      1027 1028
Direct integral decompositions into irreducible representations      1031
Direct integral decompositions of a representation      1008
Direct integral decompositions of bounded operators      1002
Direct integral decompositions of Hilbert spaces      1000 1027
Direct integral decompositions of states      1008
Direct integral decompositions of the commutant      1021
Direct integral decompositions of vectors      1000
Direct integral decompositions of von Neumann algebras      1009
Direct integral decompositions, central      1028
Direct integral decompositions, relative to a maximal abelian algebra      1030 1031
Direct integral decompositions, relative to an abelian algebra      1025—1031
Direct integral decompositions, uniqueness of      1028—1030
Direct integrals      998—1025
Direct integrals of bounded operators      1002
Direct integrals of faithful states      1012
Direct integrals of Hilbert spaces      1000
Direct integrals of normal states      1013
Direct integrals of projections      1014
Direct integrals of representations      1008
Direct integrals of states      1008
Direct integrals of tracial states      1012
Direct integrals of vectors      1000
Direct integrals of von Neumann algebras      1009
Direct sum of Hilbert spaces      121 123
Direct sum of operators      122 124
Direct sum of representations      281 734 738
Direct sum of von Neumann algebras      336
Directed system of C*-algebras      863—865 886 887
Directed system of Hilbert spaces      886 887
Directed system of simple C*-algebras      865
Discrete crossed product      see “Crossed product”
Division algebra      180
Dixmier approximation theorem      504 523
Double commutant theorem      326
Dual cones      704 705
Dual group of $\mathbb{R}$      192
Dual group of $\mathbb{T}_1$      231
Dual group of $\mathbb{Z}$      230
Dual module      771 773
Dual normal module      771 932
Dual representation      936 957 966 968
Dual space of a C*-algebra      712 719 721 726 773
Dual space, algebraic      2
Dual space, Banach      44
Dual space, continuous      30 43
Dual space, second      43 45
Duality theorem (for crossed products)      936 937 957 970
Eigenvalue      109
Eigenvalue list      914 916
Eigenvector      108
Eigenvector, approximate      178 179 183
Equivalence of function representations      263
1 2 3 4
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