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Dunford N., Schwartz J., Bade W.G. — Linear operators. Part 2
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Название: Linear operators. Part 2Авторы: Dunford N., Schwartz J., Bade W.G.Аннотация: In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V ↦ W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication. An important special case is when V = W, in which case the map is called a linear operator, or an endomorphism of V. Sometimes the definition of a linear function coincides with that of a linear map, while in analytic geometry it does not.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1963Количество страниц: 986Добавлена в каталог: 18.02.2014Операции: Положить на полку |
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Heine — Borel theorem (17) Heinz, E. 612 933 935 Heinz, inequality of X.9 (935) Heisenberg, W. 1264 Helly, E. 81 86 880 891 Helson, H. 385 1160 1161 Hensel, K. 607 Herglotz, G. 865 1274 Hermitian matrix, definition (561) Hermitian operator, definition IV.18.72 (850) X.4.1 Hettinger, E. 79 80 85 539 609 926 927 928 929 936 1269 1584 Hewitt, E. 233 373 379 381—882 384—385 387 Heywood, P. 1615 Hilb, E. 608 1583 1584 1585 1589 1590 Hilbert cube see also "Hilbert space" Hilbert cube, as a fixed point in space V.10.2—3 (453—454) Hilbert cube, definition and compactness IV.13.70 (350) (453) Hilbert proper value integral XI.7.8 (1059) Hilbert space, adjoint of an operator VI.2.9—10 (479—480) Hilbert space, characterizations of (393—394) Hilbert space, definition IV.2.26 (242) (1773) Hilbert space, finite dimensional IV.2.1 (288) IV.3 Hilbert space, general, additional properties IV.15 (3701 Hilbert space, remarks Oil (372—373) Hilbert space, study of IV.4 Appendix Hilbert — Schmidt operators XI.6 Hilbert — Schmidt operators, completeness of eigenfunctions XI.6.80 (1041) XI.6.31 Hilbert — Schmidt operators, definition XI.6.31 (1042) Hilbert, D. 79—80 372 461 531—532 538—539 608 926 1083 1268 1584 1589 1590 1773 Hildebrandt, T.H. 81 85 92—93 233 373 380 388 391 392 609 1274 Hill, G.W. 1497 Hille — Yosida — Phillips theorem on the generation of semi-groups VIII.1.18 (624) Hille, E. 80 92 543 606 608 610 612 624 726—727 729 883 1118 1162 1274 1628 Hirschman, I.I. 728 1183 Hobson, E.W. 383 1583 Hoelder inequality III.8.2 (119) Hoelder inequality, conditions for equality in III.9.42 (173) Hoelder inequality, generalizations of VI.11.1—2 (527) VI.11.13—18 Hoelder, E. 119 373 612 Hoermander, L. 1166 1170 Homeomorphism, condition for I.5.8 (18) Homeomorphism, definition I.4.15 (13) Homomorphism, between algebras (40) Homomorphism, between Boolean algebras (43—44) Homomorphism, between groups (851 Homomorphism, between rings (39) Homomorphism, natural, between linear spaces (38) Hopf, E. 669 670 722 728 729 1274 Hopf, H. 47 467 Horn, A. 610 1079 Hotta, J. 466 Hukuhara, M. 474 Hurewicz, W. 467 722 729 Hurwitz, W.A. 462 Hyers, D.H. 92 471 609 Hypergeometric series and equation XIII.8 (1509) Ideal(s), existence of maximal (39) Ideal(s), in a ring (38) Ideal(s), in an algebra (40) Ideal(s), of operators (552—538) (611) Idempotent element, definition (40) Idempotent operator or projection, definition (37) Imaginary part of a complex number, definition (4) Inaba, M. 474 Independent, linearly (36) Index, definition VII.1.2 (556) Indexed set (3) Inequalities, applications to other inequalities VI.11 (526) Inequalities, M. Rlesz convexity theorem VI.10.11 (525) Inequalities, remarks on (541) Infimum, limit inferior of a sequence of sets (126) Infimum, limit interior of a set or sequence of real numbers (4) Infimum, of a set of real numbers (3) Infinitesimal generator, of a group (627—628) Infinitesimal generator, of a semi-group of operators, definition VIII.1.6 (619) Infinitesimal generator, of a semi-group of operators, functions of VIII.2 Infinitesimal generator, of a semi-group of operators, perturbation of VIII.11.19 (631) Infinitesimal generator, study of VIII.1 Ingleton, A.W. 88 400 Inner product in a Hilbert space IV.2.26 (242) Integrable function, conditions for integrability III.2.22 (117) III.3 III.6 IV.8 IV.10.9—10 Integrable function, definition III.2.17 (112) IV.10.7 Integrable function, properties III.2.18—22 (113—117) IV.10.8 Integrable function, simple function, definition III.2.13 (108) Integrable function, simple function, properties III.2.14—18 (108—113) Integral, change of variables III.10.8 (182) Integral, countable additive case I1I.6 Integral, extension to positive measurable functions (118—119) Integral, finitely additive raise III.2—3 III.2.17 Integral, integration by parts III.6.22 (154) Integral, line integral (225) Integral, summability of IV.13.78—101 (351—356) Integral, with operator valued measure X.I. (893) Integral, with vector valued measure IV.10.7 (328) Interior mapping principle II.2.1 (55) Interior mapping principle, discussion of (83—85) Interior of a set I.4.1 (10) Interior point I.4.1 (10) Internal point, definition V.1.6 (410) Intervals, definitions (4) III.5.15 Invariant measures V.11.22 (460) VI.9.38—44 Invariant metric, in a group (90—91) Invariant metric, in a linear space II.1.10 (51) Invariant set (3) Invariant subgroup (35) Invariant subspace, definition of X.9 (929) Invariant subspace, reducing an operator X.9 (929) Inverse function and inverse image (3) Inverse of an operator and adjoints VI.2.7 (479) Inverse of an operator and adjoints, existence and continuity of VII.6.1 (584) Inverting sequence of polynomials VIII.2.12 (650) Involution, in a B-algebra IX.1 1 Involution, in an algebra (40) Ionescu Tulcea, C.T. 926 Irregular singularity of a differential equation XIII.6 (1432) (1434) Isolated spectral point VII.3.15 (571) Isometry, discussion of (91—82) Isometry, embedding of a B-space into its second conjugate space II.3.18—19 (66) Isometry, isomorphism and equivalence II.3.17 (65) Isomorphism see also "Homomorphism" Isomorphism, topological see "Homeomorphism" Iyer, V.G. 399 Izumi, S. 235 382 388 392 543 552 Jackson, D. 1589 Jacobi, C.G.J. 1275 1512 Jacobson, N. 48 985 James, R.C. 88 98 94 393—394 472—478 Jamison, S.L. 612 Jerison, M. 397 473 Jessen see "Fubini — Jessen theorems" Jessen, B. 207 209 235 530 Jordan canonical form for a matrix VII.2.17 (563) Jordan curve (225) Jordan decomposition, of a measure III.4.7 (128) III.4.11 Jordan decomposition, of an additive real set function III.1.8 (98) Jordan, C. 98 392 Jordan, P. 393—394 Jost, R. 1568 1626 Julia, G. 934 Kac, M. 406 407 Kaczmarz, S. 94 Kadison, R.V. 385 395 397 Kahane, J.P. 1161 Kakutani see "Markov — Kukutani theorem" Kakutani, S. 86 90 235 380 384 386 393—394 395 396 456—457 460 462 463 471 473 539 541 554 715 728—730 1152 Kamke, E. 47 Kantorovitch, L.V. 233 373 386 388 395 540 543 Kaplansky, I. 384—385 396 882 884 886 934 935 1161 Kaplansky, theorem on IX.4.20 (882) Karaseva, T.M. 1587 Karlin, S. 98 94 Kato, T. 612 935 Katznelson, Y. 1161 Kay, I. 1622 1626 Kaz, I. 1590 Keldys, M.V. 611 1163 Kelley, J.L. 47—48 382 385 397 398 486 554 884 927 929 Kellogg, O.D. 470 Kemble, E.C. 1592 Kernel, convergence of III.12.10—12 (219—222) IV.13C IV.14 Kernel, of a homomorphism (39) IV.13C IV.14 Kerner, M. 92 Khintchine, A. 729 Kinoshita, A. 471 Klee, V.L. 87 90 460—461 466 Kleinecke, D.C. 553 610 612 Kneser, A. 1463 1588 1590 1592 Knopp, K. 48 536 Kober, H.A. 554 Kodaira theorem XIII.2.26 (1302) Kodaira, K. 927 1152 1301 1302 1351 1355 1364 1586 1587 1589 1590 Koethe, G. 84 399 465 Kolmogoroff, A. 91 385 388 Komatuzaki 554 Koopman, B.O. 728 827 929 Koosis, P. 1161 Kostyucenko, A. 94 1587 Kozlov, V. 94 Krackovskii, S.N. 473 611 Kramer, H.P. 612 Kramer, V.A. 612 Kramers, H.A. 1592 1614 Krasnosel'skii, M.A. 400 611 1270 1273 1587 1591 Krein — Milman theorem, on extremal points V.8.4 (440) Krein — Smulian theorem, on V.5.7 (429) Krein — Smulian theorem, on convex closure of a weakly compact set V.6.4 (434) Krein, M. 94 387 395 396 397 429 434 440 461 463 465—466 611 612 Krein, M.G. 1160 1163 1270 1273 1587 1590 1591 1622 1626 Krein, S. 395 396 397 Kryloff, N. 780 Kuerschak, J. 79 Kuller, R.G. 395 Kunisawa, K 391 Kuratowski, C. 83 Lacunary series, definition IV.I4.63 (366) Lagrange, J.L. 372 1582 1588 Laguerre, E.N. 607 Lalesco, T. 1081 1162 Lamson, K.W. 35 Landsu, E. 80 1591 Langer, R.E. 1592 Langlsnds, R.P. Errata-p.5 Laplace and Laplace — Stieltjes transform VIII.2.1 (642) LaSalle, J.P. 91 399 Latshaw, V.V. 1589 Lattice, definitions (43) Laurent expansion (229) Lax, P.D. 88 1635 1748 Leader, S. 233 Least upper bound, essential III.1.11 (100) (899) Least upper bound, in a partially ordered set I.2.3 (4) Least upper bound, in the real numbers (3) Lebesgue — Stieltjes measure on an interval (143) Lebesgue, decomposition theorem III.4.14 (132) (233) Lebesgue, dominated convergence theorem III.3.7 (124) III.6.16 IV.10.10 Lebesgue, extension theorem III.5.17—18 (142—143) Lebesgue, H. 80 124 132 143 151 213 232 284 390 Lebesgue, measure, in n-dimensional space III.11.6 (188) Lebesgue, measure, on an interval (143) Lebesgue, set III.12.9 (218) Lebesgue, spaces see " Lefschetz, S. 47 467 Legendre, A.M. 1512 Leja, P. 79 Lengyel, B.A. 927 928 929 Leray, J. 84 470 609 Levi, B. 373 Levinson, N. 1266 1433 1434 1498 1503 1587 1590 1591 1592 1622 Levitan, B.M. 1587 1588 1590 1616 1622 1623 1624 1625 1626 1628 Levy, P. 407 881 Lezanski, T. 610 Lidskii, V.B. 1587 1591 Lie, S. 79 Lifsic, I.M. 612 LIMIT see also "Convergence" Limit, Banach II.4.22—23 (73) Limit, inferior (or superior), of a sequence of sets III.4.3 (126) Limit, inferior (or superior), of a set or sequence of real numbers (4) Limit, limit of a set I.4.1 (10) Limit, weak, definition II.3.25 (67) Limit, weak, in special spaces IV.15 Limit, weak, properties II.3.26—27 (68) Lindeloef theorem I.4.14 (12) Lindeloef, E. 12 1043 1115 Lindgren, B.W. 406 Line integral, definition (225) Linear dimension (91) Linear functional (38) see Linear manifold (36) see Linear operator (36) see Linear space I.11 Linear space, normed II.3.1 (59) see Linear space, topological II.1.1 (49) Linear transformation (36) see Linearly independent (36) Lions, J.L. 1724 1726 Liouville, J. 1291 1581 1582 1583 Lioville theorem (231) Littlewood, J.E. 78 531—532 541 718 1004 1006 1007 1076 1147 1177 1181 1183 1184 1591 Livingston, A.E. 399 Livsic, M.S. 611 1164 1587 Localization of series, definition (359) Locally compact space, definition 1.5.5 (17) Locally convex space, definition V.2.9 (417) Locally convex space, local convexity, of V.3.3 (419) Locally convex space, local convexity, of V.5.5 (428) Locally convex space, separation of convex sets in V.2.10—13 (417—418) Loewig, H. 372 373 Loewner, K. 407 Loomis, L.H. 79 882 886 883 927 1145 1149 1152 1160 1161 1274 Lorch, E.R 88 94 393—394 407 554 609 728 884 927 Lorentz, G.G. 84 400 543 Lower bound for an operator XII.5.1 (1240) Lumer, G. 931 933 Maak, W. 386 MacDuffee, C.C. 606 607 Mackey, G.W. 393—394 554 1160 1161 MacLane, S. 48 Macphail, M.S. 93 Maddaus, I. 93 548 552 Maeda, F. 395 1274 Malliavin, P. 1161 Mandelbrojt, S. 1161 Manifold, closed linear, spanned by a set II.1.4 (50) Manifold, in a linear space (36) see Manifold, orthogonal, in Hilbert space IV.4.3 (249) Mapping see also "Function" Mapping, interior principle II.2.1 (55) Mapping, interior principle, remarks on (83—85) Marcenko, V.A. 1587 1590 Marcinkiewicz, J. 720 1166 1180 1182 Marinescu, G. 609 Markouchevitch, A. 94 Markov process, application of uniform ergodic theory to VIII.8 Markov process, definition (659) Markov — Kakutani theorem, on fixed points of affine maps V.10.6 (456) Markov, A. 380 456 471 Martin, R.S. 79 610 883 Martin, W.T. 406 Marumaya, G. 406
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