Köthe G. — Topological vector spaces II :: Электронная библиотека попечительского совета мехмата МГУ

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Köthe G. — Topological vector spaces II

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Название: Topological vector spaces II

Автор: Köthe G.

Аннотация:

In the preface to Volume One I promised a second volume which would contain the theory of linear mappings and special classes of spaces important in analysis.
It took me nearly twenty years to fulfill this promise, at least to some extent. To the six chapters of Volume One I added two new chapters, one on linear mappings and duality (Chapter Seven), the second on spaces of linear mappings (Chapter Eight). A glance at the Contents and the short introductions to the two new chapters will give a fair impression of the material included in this volume. I regret that I had to give up my intention to write a third chapter on nuclear spaces. It seemed impossible to include the recent deep results in this field without creating a great further delay.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1979

Количество страниц: 331

Добавлена в каталог: 02.02.2006

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Предметный указатель

-space      110
$(\mathcal{D}\mathcal{F}\mathcal{M})$       304
$(\mathcal{F})$ , $(\mathcal{F}'_c)$ , $(\mathcal{F}\mathcal{M})$       303
$A_1\boxtimes A_2$       211
$A_1\otimes_{\varepsilon} A_2$       277
$A_1\tilde{\otimes}_{\pi} A_2$       187
$A_1\tilde{\otimes}_{\varepsilon} A_2$       275
$A_1\varepsilonA_2$       277
$B(E\times F)$ , $B(E\times F, G)$       153
$B(\mathfrak{T})$ -space      27
-complete      26
$E\otimes_{1n}F$       266
$E\otimes_{\pi}F$       111
$E\otimes_{\varepsilon}F$ , $E\tilde{\otimes}_{\varepsilon}F$       243
$E\tilde{\otimes}_{\pi}F$       179
$E\varepsilonF$ , $\varepsilon(E, F)$       242
      134
$H_{\lambda}$ -space      119
      290
      292
$l^1_A{F}$       198
$L^p(\mathbb{R}, \mu)$       258
$L_{\chi,\mu}^1$ , $L_{\chi,\mu}^1{F}$       199
$p\times q$       176
$P_{\lambda}$ -space      117
$\bar{E}$       44
$\beta(S)$       258
$\lambda$ -metric approximation property      260
$\lambda(F)$       291
$\lambda{F}$       196
$\mathcal{B}$ , $\mathcal{B}_s$       50
$\mathcal{B}(E\times F)$ , $\mathcal{B}(E\times F, G)$       154
$\mathcal{B}\mathcal{O}$       78
$\mathcal{B}_{\mathfrak{M},\mathfrak{N}}(E\times F, G)$       168
$\mathcal{C}^l(c_0),$ \mathcal{C}^l(c)$      51
$\mathcal{C}^l(\mathcal{B})$ , $\mathcal{C}^l(\mathcal{B}_s)$       50
$\mathcal{C}^l(\mathcal{P})$ , $\mathcal{C}^l(\mathcal{I}\mathcal{P})$ , $\mathcal{C}^l(\mathcal{I}\mathcal{P}_s)$       50
$\mathcal{C}^r(\mathcal{A})$ , $\mathcal{C}^r(\mathcal{T})$ , $\mathcal{C}^r(\mathcal{U})$       76
$\mathcal{E}$       167 242
$\mathcal{I}\mathcal{P}_s$       50
$\mathcal{K}(R)$       257
$\mathcal{L}(\mathbb{R}) = L^{\infty}(\mathbb{R}, \mu)$       259 308
$\mathcal{L}_p$ -space, $\mathcal{L}_{p,\lambda}$ -space      228
$\mathcal{N}$       78
$\mathcal{U}$       76
$\mathfrak{B}(E\times F)$ , $\mathfrak{B}(E\times F, G)$       154
$\mathfrak{B}_{\mathfrak{M},\mathfrak{N}}(E\times F, G)$       166
$\mathfrak{C}(E, F)$       200
$\mathfrak{C}_p(E, F)$       200
$\mathfrak{H}(H_1, H_2)$       212
$\mathfrak{J}(E\times F)$       294
$\mathfrak{L}(E, F)$       1
$\mathfrak{L}^I(E, F)$       304
$\mathfrak{L}_{\mathfrak{M},\mathfrak{N}}(E_s, F_s)$       134
$\mathfrak{L}_{\mathfrak{M}}(E, F)$       131
$\mathfrak{N}(E, F)$       214
$\mathfrak{T}^t$       44
$\mathfrak{T}^u$       73
$\mathfrak{T}_A$       95
$\mathfrak{T}_b$       166
$\mathfrak{T}_c$       201
$\mathfrak{T}_s$       166
$\mathfrak{T}_{cf}$       73
$\mathfrak{T}_{co}$       232
$\mathfrak{T}_{in}$       266
$\mathfrak{T}_{\epsilon}$       268
$\mathfrak{T}_{\mathfrak{M},\mathfrak{N}}$       166
$\mathfrak{T}_{\mathfrak{M}}$       131
$\mathfrak{T}_{\pi}$       177
$\mathfrak{T}_{\varepsilon}$       167
$\mathfrak{W}(E, F)$       205
$\mathfrak{X}(E\times F)$       156
$\mathfrak{X}(E\times F, G)$       156
$\mathfrak{X}^{(\mathfrak{M})}(E\times F)$       156
$\mathfrak{X}^{(\mathfrak{M})}(E\times F,G)$       156
$\mathfrak{X}^{(\mathfrak{M})}_{\mathfrak{M},\mathfrak{N}}(E\times F,G)$       168
$\mathfrak{X}^{(\mathfrak{M},\mathfrak{N})}(E\times F)$       156
$\mathfrak{X}^{(\mathfrak{M},\mathfrak{N})}(E\times F,G)$       156
$\pi$ -norm      178
$\Psi$       181
$\sigma$ -locally topological      301
$\varepsilon$ -hypocontinuous bilinear form      244
$\varepsilon$ -hypocontinuous trilinear form      272
$\varepsilon$ -product      242
$\varepsilon$ -tensor product      243
$\varepsilon$ -topology      266
      90
      160
(DFM)-space      303
(S)-space      45
(u)-space      77
Adasch, N.      1 44 46 47 48 49 80 93 97 144 301
Adasch’s open mapping theorem      48
Approximation property      222 232
Aronszajn, N.      230
Associated barrelled space      44
Associated ultrabornological space      73
B-complete      26
Baire space      25 43
Baker, J.W.      100 105 118
Banach disk      70
Banach — Mackey theorem      135 168
Banach, S.      235 249 253
Banach-Steinhaus theorem      141 142
Basis      248
Basis, problem      253
Batt, J.      210
Bessaga, C.      249
Bi-equicontinuous topology      167
Bibounded topology      166
Bierstedt, K.D.      244 246 257 289 300
Bounded approximation property      26
Bounded mapping      160
Bourbaki, N.      9 43 153 155 163 200 258
Browder, F.      80 105 124
Buchwalter, H.      300 301 302 303
C(X, E)      286
Canonical bilinear mapping x      173
CB(S)      257
Closable      81
Closed for the Mackey convergence      15
Closed mapping      34
Co-extension property      228
Compact extension property      227
Compact lifting property      229
Compact mapping      200
Compatible topology      264
completely continuous      207
Conjugate element      211
Continuity theorems      158 159 160 161
Continuous contraction      87
Continuous left inverse      115
Continuous refinement      96
Continuous right inverse      115
Countably barrelled      142
Cross, R.W.      112
d(E, F)      228
Davie, A.M.      235 244
De Wilde, M.      1 53 54 56 65 66 67 69 70 73 75 78 79 203 249 250 253 284
De Wilde’s closed-graph theorem      57
Dense mapping      80
Densely defined mapping      80
Detachable      118
Diestel, J.      317 319
Dieudonne, J.      22 43 255
Distance coefficient      228
Domain of definition      34
Duality theorems of Buchwalter      301 302
Dugundji, J.      231
Dunford — Pettis property      210

D[M, N]      174
e      74
Eberhardt, V.      46 49 76 78 116
Edwards, R.E.      210 249
Eidelheit, M.      125 126
Enflo, P.      130 235 244 247 248 253 260 262 264
Equibounded      160
Equicontinuous basis      248
Equicontinuous topology      167
Equihypocontinuous      158
Ernst, B.      301
Extended kernel      81
Fast convergent      70
Fast convergent, null sequence      71
Figiel, T.      260
Fillmore, P.A.      111
Finite section      292
Fully solvable      126
Gantmacher, V.      205
Garnir, H.G.      203
Goldberg, S.      65 106 124 210
Goodner, P.      118
Graph topology      95
Grathwohl, M.      76
Grothendieck, A.      8 19 21 22 44 53 54 61 63 68 120 130 131 140 143 152 153 160 164 165 169 171 176 183 193 202 204 210 214 224 232 234 235 243 260 264 305 315 317 318 319
Hagemann, E.      31
Hahn, H.      113
Hasumi, M.      118
Hellinger — Toeplitz theorem      40 41
Hellinger, E.      40
Helly, E.      113
Henriques, G.      255
Hilbert — Schmidt mapping      212
Hilbert — Schmidt norm      212
Hogbe — NIend, H.      232 246 248
Hollstein, R.      274 302 304
Holub, J.R.      285 286
Homomorphism theorem      8
Homomorphism theorem for (B)-spaces      17
Homomorphism theorem for (F)-spaces      18
Husain, T.      27 28 49 142
Hypercomplete      31
Hypocontinuous      155 166
Ichinose, T.      286
Inductive tensor product      266
Inductive tensor product, topology      266
Infinite-nuclear      226
Infinite-nuclear norm      227
Infra-(s)-space      44
Infra-(u)-space      77
Infra-Ptak space      26
Injective tensor product      266
Injective topology      266
Integral bilinear form      294
Integral mapping      304
Integral norm      294
Invariant subspace      230
Johnson, W.B.      131 260 261 262
Kaballo, W.      280
Kalton, N.J.      1 50 51 52 53 255
Kalton’s closed-graph theorems      50 51 53
Kato, K.      65 66 210
Kaufmann, R.      118
Kelley, J.L.      1 31 32 49 79 118
Komura, Y.      1 44 45 76 78
Komura’s closed graph theorem      45
Kothe, G.      17 21 31 40 43 47 67 118 119 120 203 297
Krein — Smulian property      31
Krishnamurthy, V.      123 124
L(E, F)      133
Lacey, E.      210
Landsberg, M.      230
Liftable      118
Lifting property      19
Lindenstrauss, J.      118 120 130 228 231 254 263
Lindenstrauss’ theorem      228
Linear equation      111
Localization theorem      67
Locally closed      15
Locally complete      135
Locally convex algebra      170
Locally sequentially invertible      15
Locally topological      301
Lomonosov, V.I.      130 231
Lotz, H.T.      296
Loustaunau, J.O.      123 124
Macintosh, A.      79
Mackey — Ulam theorem      72
Mahowald, M.      38 50 52 53 75
Marti, J.T.      254
Martineau, A.      54 79
Maximal slight extension      91
McArthur, C.W.      254
Meise, R.      244 246 289 300
Metric approximation property      260
Mitiagin, B.S.      319
Mochizuki, N.      122
Nachbin, L.      118
Nakamura, M.      205
Nearly continuous      36
Nearly open      24
Neubauer, G.      170
Neumann, J.von      176
Newns, H.F.      249
Niethammer, W.      127
Nuclear mapping      214
Nuclear norm      215
Open mapping theorem of Adasch      47 48
Partition of unity      255
Pelczynski, A.      120 130 210 228 247 249 260
Persson, A.      49
Pettis-integral      318
Phillips, R.S.      117 258 260
Pietsch, A.      183 196 216 289 292 314 319
Pitt, H.R.      208
Powell, M.      74 76
Precompact mapping      200
Prenuclear      314
Principle of uniformed boundedness      135
Projective norm      178
Projective tensor product      177
Projective topology      177
Ptak space      26
Ptak, V.      1 23 24 27 30 37 41 49 67
Q[A]      81
Radon — Nikodym property      319
Raikow, D.A.      54 78
Randtke, P.J.      226 228
Reduced locally convex kernel      192
Regular contraction      86
Regular mapping      80
Riemann, B.      289
Robertson, A.and W.      1 14 48 49 67 79 144 145 183 184
Rosenthal, H.P.      210 228
Saturated, saturated cover      131
Scalar net      31
Scalarly complete      31
Schaefer, H.      176 200
Schatten, R.      131 176 297 317
Schauder basis      248
Schauder, L.      130 202 254 269
Schmets, J.      203
Schwartz, L.      43 54 79 131 176 193 232 243 260 271 284 289
Separately continuous      158
Sequentially closed mapping      56
Sequentially continuous      157
Sequentially invertible      13
Sequentially separable      254
Simons, S.      218
Simple topology      133 166

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