Kadison R.V., Ringrose J.R. — Fundamentals of the Theory of Operator Algebras (vol. 2) Advanced Theory :: Электронная библиотека попечительского совета мехмата МГУ

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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.

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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

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Предметный указатель

Tensor product of Hilbert spaces      125 135
Tensor product of irreducible representations      848
Tensor product of maximal abelian von Neumann algebras      829
Tensor product of representations      848
Tensor product of represented C*-algebras      800—812
Tensor product of unbounded operators      812 836—845
Tensor product of vectors      135
Tensor product of von Neumann algebras      800 812—845
Tensor product, algebraic      139 846 849
Tensor product, associativity of      136 146 802 813 847
Tensor product, center of      800 829 878
Tensor product, commutant of      800 812 821 828 843
Tensor product, predual of      818
Tensor product, spatial      800 846—850
Tensor product, type of      800 812 829—836
Tensor product, universal property of      125 135 139
Tomita's theorem      472 591 607 625 631 638 640
Topological divisor of zero      229
Topological group      789
Topology, bounded weak-operator      995
Topology, coarser (weaker)      29
Topology, induced by semi-norms      17
Topology, initial      13
Topology, Jacobson      792
Topology, locally convex      16 23
Topology, norm      35 66
Topology, strong-operator      113 304 305 329 380 456
Topology, ultraweak      482
Topology, weak-operator      304 305 306 371 456
Topology, weaker (coarser)      29
Totally disconnected      222 374
Trace      462
Trace class      543
Trace class operator      462 543
Trace norm      545 895
Trace vector      436 471
Trace vector, generating      471 472 501
Trace, center-valued      504 508 509 527 535 537
Trace, faithful      505
Trace, normalized      289
Trace, numerical      505
Tracial state      505 506 537 575 611 848 870
Tracial weight      504 537—545 575
Tracial weight on $\mathscr{B}(\mathscr{H})$       543 576 578
Tracial weight, relatively invariant      976 983
Transformation, linear      see “Operator” “Unbounded
Transformation, unitary      104
Transitivity      332 727
Transitivity of the automorphism group      904 907
Triangle inequality      35
Type decomposition (of a von Neumann algebra)      399 422
Type decomposition (of a von Neumann algebra) and direct integrals      1015 1028
Type decomposition (of a von Neumann algebra) of tensor products      800 812 829—836
Type decomposition (of a von Neumann algebra) of the commutant      585—590
UHF algebra      see “Uniformly matricial algebra”
Ultraweak continuity (criteria for)      720 722 725 726 748
Ultraweak topology      482
Unbounded operator, adjoint of      157 594
Unbounded operator, affiliated      342 344
Unbounded operator, closable (preclosed)      155 593
Unbounded operator, closed      155 357 593
Unbounded operator, closure of      155
Unbounded operator, conjugate-linear      593
Unbounded operator, core of      155
Unbounded operator, densely defined      155 593
Unbounded operator, domain of      154 155
Unbounded operator, extension of      155
Unbounded operator, graph of      155
Unbounded operator, invertible      595
Unbounded operator, maximal symmetric      160
Unbounded operator, multiplication      see “Multiplication operator”
Unbounded operator, normal      see “Normal operator”
Unbounded operator, positive      357 840
Unbounded operator, preclosed (closable)      155 593
Unbounded operator, products of      157 352
Unbounded operator, self-adjoint      see “Self-adjoint operator”
Unbounded operator, spectrum of      357
Unbounded operator, sums of      157 352
Unbounded operator, symmetric      160
Unbounded operator, tensor product of      812 836—845
Unbounded operator, von Neumann algebra generated by      349 354
Unbounded similarity theory      625

Uniform boundedness (principle of)      64 65 74
Uniform multiplicity, bounded normal operator of      703
Uniform multiplicity, representation of      685 688
Uniform multiplicity, set of      673 685
Uniform structure in a linear topological space      14
Uniform structure in a normed space      35
Uniformly convex Banach space      67 161
Uniformly matricial algebra      759—766 889—895 904—920
Uniformly matricial algebra, algebraically equivalent states of      909
Uniformly matricial algebra, automorphic states of      907 909
Uniformly matricial algebra, criterion for      893
Uniformly matricial algebra, isomorphism classes of      889 890 891 893
Uniformly matricial algebra, isomorphism invariant for      890 891 893
Uniformly matricial algebra, primary states of      889 905
Uniformly matricial algebra, product states of      877 904
Uniformly matricial algebra, pure states of      904 907
Uniformly matricial algebra, quasi-equivalent representations of      905 909
Uniformly matricial algebra, quasi-equivalent states of      889 905 909
Uniformly matricial algebra, transitive action of automorphism group      907
Union of projections      111
Unit ball      36
Unit element      174 236
Unitary element (of a C*-algebra)      237 242 767 768
Unitary element (of a C*-algebra), exponential      275 286 287 288 313 314 728 767 768
Unitary equivalence of bounded normal operators      670 688 703
Unitary equivalence of representations of a C*-algebra      280 697 730 736 740
Unitary equivalence of representations of an abelian C*-algebra      670—689 702
Unitary equivalence of von Neumann algebras      469 470 661 662 663 697
Unitary group      237 286 287
Unitary implementation (of * isomorphisms)      469 661 663 664 671 696—700
Unitary implementation theorem      454 469
Unitary operator      103 313
Unitary representation      282 367 710
Unitary transformation      104
Universal normal representation      458 459
Universal representation      281 711—727 735 744 746 766 768 770 772 773 777 779 780 790 793
Unordered sums      25—28
Vector state      256 281 289 298 302 467 469 478 480 492 496 783
Vector state space      782
von Neumann algebra      308; see also “Factor”
von Neumann algebra of type      11 422 447 589 976 985 989
von Neumann algebra of type $\mathrm{II}_1$       422 588 589
von Neumann algebra of type $\mathrm{II}_\infty$       422 447 589
von Neumann algebra of type $\mathrm{I}_\mathrm{n}$       422 432 447 589 699
von Neumann algebra of type I      399 422 426—432 447 584 588 589 660—665 689 699 700
von Neumann algebra of type II      447 589 699
von Neumann algebra of type III      411 422 447 588 589 937 976 985 989
von Neumann algebra, abelian      308 310 340—366 665—670 700 701
von Neumann algebra, continuous      424 426
von Neumann algebra, countably decomposable      338 339 380 449
von Neumann algebra, decomposable      999 1009 1010 1011
von Neumann algebra, discrete      424
von Neumann algebra, finite      411 447 449 517
von Neumann algebra, generated by a bounded normal operator      700 701
von Neumann algebra, generated by an unbounded normal operator      349 354
von Neumann algebra, infinite      411
von Neumann algebra, matricial      895 896
von Neumann algebra, maximal abelian      see “Maximal abelian algebra”
von Neumann algebra, normal      930 1046
von Neumann algebra, properly infinite      411 449
von Neumann algebra, purely infinite      411
von Neumann algebra, semi-finite      424 589 592 618 623 1045
von Neumann algebra, type decomposition of      see “Type decomposition”
W*-algebra      498 500 794
w*-topology      31
Weak * topology      31 43 45 46 48 68
Weak topology, induced by a family of linear functionals      28 29
Weak topology, the weak topology      30 43 47 66
Weak-operator topology      304 305 306 371 456
Weakly measurable mapping      1019
Wedge product      933
Weierstrass approximation theorem      221
Weight      486 490 500
Weight, faithful      487
Weight, normal      487
Weight, semi-finite      487
Weight, tracial      504 537—545 575 576 578
Wick-ordered monomial      934
Wick-ordered product      795
Wiener's Tauberian theorems      233
Word      437
Word, reduced      437

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