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Berberian S.K. — Baer *-Rings
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Название: Baer *-RingsАвтор: 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: 1972Количество страниц: 296Добавлена в каталог: 09.03.2011Операции: Положить на полку |
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13 55 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), 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 182 Type 195 199 201 238 263 Type 94 Type 94 Type 94 170 199 Type 94 Type 112 116 119 160 170 197 209 261 263 Type 119 197 199 201 209 232 263 Type 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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