Berberian S.K. — Baer *-Rings :: Электронная библиотека попечительского совета мехмата МГУ

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Berberian S.K. — Baer *-Rings

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Название: Baer *-Rings

Автор: Berberian S.K.

Аннотация:

A systematic exposition of Baer *-Rings, with emphasis on the ring-theoretic and lattice-theoretic foundations of von Neumann algebras. Equivalence of projections, decompositio into types; connections with AW*-algebras, *-regular rings, continuous geometries. Special topics include the theory of finite Baer *-rings (dimension theory, reduction theory, embedding in *-regular rings) and matrix rings over Baer *-rings. Written to be used as a textbook as well as a reference, the book includes more than 400 exercises, accompanied by notes, hints, and references to the literature.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1972

Количество страниц: 296

Добавлена в каталог: 09.03.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$B_{p}^{*}$ -algebra      13
$\aleph$ -addability      55
$\aleph$ -uciditivity of equivalence      55
(C)      256 216 218
(EP)-axiom      43 241
(P)      62
(PS)-axiom      244
(PSR)-axiom      70
(SR)-axiom      66 131
(SSR)-axiom      76
(UPSR)-axiom      70 239
(US)-axiom      233
(VWEP)-axiom      43
(VWSR)-axiom      254
(WEP)-axiom      43
(WSR)-axiom      66
*-algebra      3 9 101 121
*-equivalence of projections      264
*-regular ring      229
*-ring      3
*-subring, Baer      22 27 44 145
*-subset      9 17
Abelian projection      90 95 113
Abelian projection, *-ring      90 95
Addability of partial isometries      55 129 131 263
Additivity of equivalence, complete      55 122 129 130 183
Additivity of equivalence, finite      6 264
Additivity of equivalence, orthogonal      55
Adjunction of a unity element      11 30 31
Algebraically equivalent idempotents      9
Algebraically equivalent idempotents, projections      9 18 66 230 232 253
ALP      28
Annihilating left (right) projection      28
Annihilator      12
ARP      28
AW*-algebra      21 24 25 43 262
AW*-algebra, commutative      40 44 209 263
AW*-algebra, equivalence in      97
AW*-algebra, generated by projections      97
AW*-algebra, real      26
AW*-embedded      26 27
AW*-factor      36 206 209
AW*-subalgebra      23 25 27 44
Baer C*-algebra      21
Baer C*-algebra, *-factor      36 201
Baer C*-algebra, *-ring      20
Baer C*-algebra, *-subring      22 27 44 145
Baer C*-algebra, ring      25
Bicommutant      16 19
Boolean algebra      19
Boolean algebra, ring      19
Bounded element      243
Bounded element, subring      243
C(T), $C_{\infty}(T)$       11
C*-algebra      11
C*-algebra, Baer      21
C*-algebra, Rickart      13
C*-sum      52
CAP      27
Cartesian decomposition      227
Category of Baer *-rings      145
Cayley transform      228 231 234
Ccntral covcr      34 252
Center      17 23
Central additivity      132
Central projection      17 18
Clopenset      40
Closed operator      216
CO      216
Coarse structure theory      87 93—96
Commutant      16 19
Commutative      44
Commutative AW*-algebra      40 44 209 263
Commutative AW*-algebra, projection      95
Commutative AW*-algebra, Rickart C*-algebra      44
Commutative AW*-algebra, weakly Rickart С*-algebra      48
Commutative AW*-algebra, С*-algebra      11
Compact operators      15 135
Comparability, generalized      77
Comparable projections      77
Complement      39 108
Complementary projections      39 108
Complementation      185 211 212
complete      25
Complete *-regular ring      25
Complete additivity of dimension      163 181
Complete additivity of equivalence      55 122 129 130 183
Complete Boolean Algebra      19
Complete direct product of *-rings      9
Complete lattice      7
Complete lattice of projections      20 21
Completely additive on projections      27 43
Continuous *-ring      92
Continuous geometry      185 232
D(e)      153 181
Diagonal operators      209
Dimension function      153 181
Direct product, complete of *-rings      9
Direct product, complete of Baer brings      25
Direct product, complete of regular Baer *-rings      237
Direct product, complete of Rickart *-rings      19
Direct summand      18 25
Discrete      92 93
Divisibility of projections      119 155
Domination of projections      6
Equivalence of idempotents, algebraic      9
Equivalence of projections      4 6 109 110
Equivalence of projections in a von Neumann algebra      109 110
Equivalence of projections in an AW*-algebra      97
Equivalent partitions      102
Exchange by a symmetry      69
Extremal partial isometry      83 135
Extremal point, of unit ball      83
Extremally disconnected space      40
Factor      36
Factorial ideal      144 146
Factorial ideal, *-ring      36
Factorial ideal, p-ideal      144 149
Faithful projection      38 96
Final projection      5
Fine structure theory      87
Finite projection      89 101 104 106 107
Finite projection, *-ring      89
Fixed-Point Lemma      7
Fundamental projection      158 159
GC      77 130 132 181
GC, orthogonal      79
Generalized comparability      77 130 132 181
GePfand — Naimark theorem      11 251 262
Homogeneous Baer *-ring      111
Homogeneous partition      102
Hyperstonian space      44
Ideal, restricted      138 142
Ideal, restricted, factorial      144
Ideal, restricted, strict      141 144 149 232
Idempotent      3 8 9 11 18 96
Infinite *-ring      89
Initial projection      5
Involution      3
Involution, proper      10
Involutive ring      3
Lattice of projections      14 29

Lattice of projections, complete      20 21
Left projection      13 28
Left-annihilator      12
Locally orthoseparable      118
lp      13 28
LP~RP      131 136 186 220 232 263
MASA      9 43
Matrix rings      97 248 253 262
Maximal abelian self-adjoint subalgebra      9
Maximal rings of quotients      284
Maximal-restricted ideal      146 186 192 201 208 209 247
Maximal-strict ideal      187 202
Minimal projection      25 96 97 118 119
Modular lattice      108 184 185 211
Morphisms      145
Multiplicity sequence      190
Normal element      9
Normal measure      44
Of a simple projection      157
Of self-adjoints      224 245
Operator with closure      214
Operators with separable range      16
Order, of a homogeneous *-ring      111
Ordering, of projections      4
Orthogonal addability of partial isometries      55
Orthogonal additivity of equivalence      55
Orthogonal GC      79
Orthogonal projections      4
Orthogonal projections, very      36 77
Orthoseparable      118 131 182
OWC      214
P*-sum      9 19 25 54 59
P, position      65
P-ideal      137 138 247
p-ideal, factorial      144 149
p-ideal, maximal      148 192
p-ideal, strict      141 149
Parallelogram law      62
Partial isometry      5 10 55 129 223 250
Partial isometry, extremal      83 135
Partially comparable      78 256
Partition      102
Partition, homogeneous      102
Partition, maximal homogeneous      102
PC      78 130 132
pd      134
Perspective projections      108—110
Polar decomposition      134
Position p      64 77
Positive element in a *-ring      70 224 242
Positive square roots      70 240
Primitive ideal      149 208
Projection      3
Projection, abelian      90 95
Projection, central      17
Projection, finite      89 101 104 106 107
Proper involution      10
Properly infinite      91 103 110
Properly nonabelian      91
Prueferring      209 263
Purely infinite      92
Purely real *-ring      231
P’, position      64 77
Quotient rings      142 186 201 246
Quotients, rings of      284
Real at infinity, ring of sequences      26 131 135 249
Real AW*-algebra      26 249
Reduced ring      19 97 101 121 141
Reduction of finite Baer *-rings      186 201
Reduction of finite i      4
Reduction of finite von Neumann algebras      208
Reduction of von Neumann algebras      208
Regular Baer *-ring      25 211 230 232 235 241 257 262 263
Regular ring      229 235 241
Restricted ideal      138 142 246 247
Restricted-simple      187 192 202
Rickart C*-algebra      13
Rickart ring      18
Rickart «-ring      12
Right projection      13 28
Right-annihilator      12
Ring      3
RP      13 28
Schroeder — Bemstein theorem      7 59 60
Schroeder — Bemstein theorem, failure of      62
SDD      213
Self-adjoint element      3
Semifinite      91
Semifinite, von Neumann algebra      97
Semisimple, strongly      186 208 222 263
Separable range, operators with      16
Similarity      9 18
Simple projection      157 257
Square roots      66 70 240
Stone representation space      19 148 149
Stone — Cech compactification      209
Stonian space      40 44
Strict ideal      141 144 149 232
Strong semisimplicity      186 208 222 263
Strongly dense domain      213
Structure theory      87
Summand, direct      18
Sums of squares      282
Symmetric *-ring      9 18 25 108 227 232 253
Symmetry      19 56 69 110
Trace      97 280
Type $II_{1}$       182
Type $II_{1}$ , factor      195 199 201 238 263
Type $II_{fin}$       94
Type $II_{inf}$       94
Type $I_{fin}$       94 170 199
Type $I_{inf}$       94
Type $I_{n}$       112 116 119 160 170 197 209 261 263
Type $I_{n}$ , factor      119 197 199 201 209 232 263
Type $I_{\aleph}$       116 119
Type I      93 95
Type I, AW*-algebra      88 118 119
Type I, Baer *-ring      110 199 201
Type I, von Neumann algebra      88 97 118
Type II      93
Type III      93 165
Ubiquitous set of projections      18
Ultimately real sequences, ring of      247 285
Unitary equivalence of projections      109 264
Unitification      30 31
Unity element, adjunction of      11 30 31
Very orthogonal      36 77
von Neumann algebra      24 100 109 110 118 141 145
Von Neumann algebra, commutative      43 209
Von Neumann algebra, embedding in      25 27 145
von Neumann algebra, finite      97 208 211 242
Von Neumann algebra, generated by projections      97
Von Neumann algebra, projections in position p’      11
Von Neumann algebra, reduction of      208
Von Neumann algebra, semifinite      97
Von Neumann algebra, Type I      88 97 118 119
Weak centrality      147 149
Weakly Rickart *-ring      28
Weakly Rickart C*-algebra      45
Weakly Rickart C*-algebra, commutative      48
Weighted shift      276
Well-directed family      181 184 185 218 222 224 226 232
WPD      134

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