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| Zelazko W. — Banach Algebras |
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| Предметный указатель |
Algebra 6
Algebra antisymmetric function 160
Algebra generated by a system K 45
Algebra of quotients 16
Algebra,  - 33
Algebra, *- 113
Algebra, Arens *- 128
Algebra, B*- 115 124
Algebra, Banach (B-) 9
Algebra, C*- 124
Algebra, complex 6
Algebra, concrete function 141
Algebra, Dirichlet 155
Algebra, function 141 165
Algebra, group 14
Algebra, Liouville 166
Algebra, locally bounded (l. b.) 32
Algebra, locally bounded (l. b.), convex (LC-) 32
Algebra, maximum modulus 165
Algebra, Montel 166
Algebra, normed 11
Algebra, primary 108
Algebra, primitive 57
Algebra, Q- 35
Algebra, quotient, of A modulo I 6
Algebra, real 6
Algebra, regular 102
Algebra, self-adjoint 103
Algebra, semi-simple 56
Algebra, symmetric 114
Algebra, topological 8
Algebra, uniform 165
Allan, G.R. 67 74 95 110 111 138
Aoki, T. 167
Arens, R. 15 18 34 65 90 91 110 111 128
Banach, S. 34
Birtel, F.T. 166
Bishop, E.A. 149 150 154 160
Bohnenblust, H.R. 53
Bonnard, M. 111
Boundary, Bishop 149
Boundary, Choquet 152
Boundary, Shilov 61
Brooks, R.M. 66 69 139
Browder, A. 87
Calculus operator 74
Calculus, symbolic 74
Calderon, A.P. 90 91
Cauchy, A. 59 71 72 88
Cech, E. 142
Choquet, G. 152 154
Closure of a subset 3
Cohen, J.P. 23 26
Component principal, of the group 28
Convex hull, closed 8
Convex hull, polynomially, of a set 42 77
Cortex of algebra 64
Cosets modulo I 6
Cousin, J.A.J. 92—94
Craw, I.G. 34 65
Dales, H.G. 110
Decomposition of Banach algebra into a direct sum of ideals 95
Decomposition, Jordan 140
Dirichlet, P, G.L. 154 155 157—160
Divisor, generalized topological, of zero 68
Divisor, topological, of zero (right, left, two-sided) 57
Diximier, J. 138
Dixon, P.G. 65 68 138
Dunford, N. 5 8 167
Edelstein, J.S. 31
Eidelheit, M. 57
Elements, almost nilpotent 68
Elements, generalized nilpotent 54
Elements, Hermitian 113
Elements, k-singular 69
Elements, left-quasi-invertible 27
Elements, left-quasi-regular 27
Elements, maximal 2
Elements, minimal 2
Elements, nilpotent 54
Elements, normal 113
Elements, permanently singular 59
Elements, positive, of A 129
Elements, quasi-invertible 26
Elements, right-quasi-regular 27
Engelking, R. 46
Family, total, of functional 7
Fremlin, D.H. 65
Frobenius, F.G. 18 19 37
Functional, multiplicative linear 25 36
Functional, non-decomposable 135
Functional, positive 120 125 142
Functions, analytic, of one complex variable to act on an element 70
Functions, entire, operates in an algebra 35
Functions, locally belonging to algebra 99
Gelbaum, B.R. 15
Gelfand, I.M. 14 17 18 34 41 43—45 47 51 54 56 66 99 102 105 112 116 117 127—132 137 149 163 165
Gill de Lamadrid, J. 16
Gleason part of algebra 158
Gleason, A.M. 87 155 158—160
Glicksberg, I. 160 164
Gramsch, B. 110
Gunning, R.C. 87 88 91 92
Haar, A. 14 33
Hadamard, J. 82
Hahn, H. 144
Hewitt, E. 23 141
Hirschfeld, R.A. 142
Hoffman, K. 145 165
Homomorphisms, *- 113
Homomorphisms, algebraic 9
Homomorphisms, natural, of A onto A|I 6
Homomorphisms, self-adjoint 113
Homomorphisms, topological 9
Ideals, left 6
Ideals, maximal 6 37
Ideals, modular 28
Ideals, modular, left or right 27
Ideals, primary 108
Ideals, prime 48
Ideals, primitive 55
Ideals, proper 6
Ideals, right 6
Ideals, smallest 100
Ideals, two-sided 6
Identity, approximate 22
Identity, approximate, left and right 22
Interior of a subset 3
Involution 112
Involution, symmetric 114
Isomorphism, algebraic 9
Isomorphism, topological 9
Johnson, B.E. 57
Jordan, C. 140 158
Kahane, J.P. 87 111
Kailin, E. 99
Karlin, S. 53
Kitainik, L.M. 68
Koethe, G. 168
Kolmogoroff, A.N. 168
Krein, M.G. 8 135 143 144 162
Kronecker, L. 1 33 41
Kuratowski, K. 2 3 6 28 61 119 125 150
Lebesgue, H.L. 13 141 157
Lemma, Kuratowski — Zorn 2
Lemma, Urysohn 4
LePage, C. 142
Levy, H. 74
Lindberg, J.A. 166
Liouville, J. 18 166
| Logarithm of an element 29
Lorch, E, R. 30 31
Malliavin, P. 107
Mallios, A. 16
Mazur, S. 16—18 34 147 168
McClure, J.P. 110
Measure probability 140
Measure, absolutely [ -absolutely] continuous 140
Measure, absolutely [-absolutely] continuous, singular, with respect to the function algebra 159
Measure, concentrated 139
Measure, Haar 14
Measure, non-negative 139
Measure, regular 140
Measure, singular [-singular] 140
Meyers, W.E. 166
Michael, E. 33 34 65 66
Milman, D.P. 8 135 143 144 162
Minkowski, H. 52
Mitiagin, B.S. 35
Montel, P. 166
Multiplication, trivial 10
Murphy, I.S. 121
Nagasawa, M. 146 149
Nagumo 30
Naimark, M.A. 14 109 116 117 128—131 137 138
Neubauer, G. 67
Nikodym, O. 141
Norm, admissible 53
Norm, F- 167
Norm, spectral 51
Norm, submultiplicative 11
Oka, K. 92—94
Operator, positive 129
Orlicz, W. 168
Phelps, R.R. 154
Point peak, of the space [algebra] 150
Point, cluster 3
Point, extremal 8
Polydisc, closed 87
Polydisc, open 87
Pontriagin, L.S. 18
Principle, local maximum modulus 94
Principle, transfinite induction 2
Product of cosets 6
Product, Arens 15
Product, topology 4
Projection 113
Przeworska-Rolewicz, D. 110
Pseudonorm, p-homogeneous 167
Quasi-inverse of element 27
Radical of algebra 54
Radius, spectral 53
Radon, J. 83 141
Raikov, I.M. 14
Representation of the algebra A 55 118
Representation, cyclic 118
Representation, equivalent 118
Representation, Gelfand 38
Representation, irreducible 55 118
Rickart, C.E. 48 55 57 69 80 110
Riemann, B. 67 110 168
Riesz, F. 138 139 141
Rings, normed 9
Rolewicz, S. 35 68 110 167
Rossi, H. 87 88 91 92
Rouche, E. 63
Sakai, S. 138
Schaefer, H. 167 168
Schwartz, J. 5 8 129 138 167
Schwarz, H.A. 120 129
Set of antisymmetry for A 161
Set of antisymmetry for A, maximal ideals 37
Set of antisymmetry for A, states of the algebra [space] 193
Set peak (local) 92
Set peak (local) of the algebra 162
Set, linearly ordered 2
Set, maximizing 61
Set, ordered 2
Set, well ordered 2
Shilov, G.E. 14 47 61—64 91 92 104 141 145 146 149 150 152 166
Singer, J.M. 164 165
Solution of the additive Cousin problem 92
Space of type 168
Space structure 49
Space, - 168
Space, bounded 167
Space, compact 4
Space, compactified, by the point at infinity 5
Space, F- 167
Space, Hausdorff 3
Space, locally bounded (l.b.) 167
Space, locally compact topological 4
Space, normal 4
Space, regular 11
Space, topological 3
Spectrum of an element 47
Spectrum, extended, of an element 67
Spectrum, joint 47 81
Stone, M.H. 5 116 117 142 147 149 162 165
Stromberg, K. 23 141
Subalgebra, self-adjoint 113
Subspace invariant, of the representation 55 118
Suciu, I. 16
Sum, direct 15 57
Sum, direct, of the family of representation 123
Sum, subdirect 57
Symbol, Kronecker 1—2
Tao-Hsing, Hsia 138
Theorem on the partition of unity 104
Theorem, Aoki — Rolewicz 167
Theorem, Bohnenblust and Karlin 53
Theorem, Cohen factorization 23
Theorem, Frobenius 18
Theorem, Gelfand — Naimark 116
Theorem, Gelfand — Naimark Representation 128
Theorem, Krein — Milman 8
Theorem, Levy 74
Theorem, Lorch 30
Theorem, Malliavin 107
Theorem, Mazur — Gelfand 17
Theorem, Nagasawa 149
Theorem, Nagumo 30
Theorem, Rossi, on local peak set 92
Theorem, Shilov — Bishop 161
Theorem, Tikhonov 4
Theorem, Weierstrass — Stone 5
Theorem, Wiener 42
Theorem, Wiener Tauberian 108
Tikhonov, A.N. 4
Titchmarsh, A.N. 82
Topology hull-kernel 49
Topology structure 49
Topology, Gelfand 43
Topology, Tikhonov 4
Transform, Gelfand 38
Transformation, Gelfand 38
Ulam, S. 149
Urysohn, P.S. 4 156
Variation, total, of a measure 139
Vector, cyclic, of representation 118
von Neumann, C.G. 130
Vood, B. 118 128 138
Waelbroeck, L. 34 67 111
Weierstrass, K. 5 116 117 147 149 162 165
Wermer, J. 160
Wiener, N. 41 65 100 108 110
Williamson, J.H. 34
Zelazko, W. 18 32—35 58 65—69 87 110 111 142
Zermelo, E. 2
Zorn, M. 2 3 6 28 61 119 125 150
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