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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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Oxtoby, J.C. 722 728 722 1152 Pais, A. 1568 Paley, R.E.A.C. 405 406 541 1177 1181 1264 Parallelogram, identity (249) Parker, W.V. 1080 Partial isometry, definition XII.7.4 (1248) Partially ordered set, bounds in I.2.3 (4) Partially ordered set, completely ordered I.3.9 (8) Partially ordered set, definition I.2.1 (4) Partially ordered set, directed set I.7.1 (26) Partially ordered set, fundamental theorem on I.2.5 (5) Partially ordered set, study of I.2 Partially ordered set, totally ordered I.2.2 (4) Partially ordered set, well ordered I.2.8 (7) Peano, G. 1588 Peck, J.E.L. 471 474 Periodic function (almost periodic function), definition IV.2.25 (242) Periodic function (almost periodic function), multiply IV.14.68 (367) Periodic function (almost periodic function), study of IV.7 Perron, O. 1078 Perturbation of bounded linear operators, remarks on (611—612) Perturbation of bounded linear operators, study of VII.6 VII.8.1—2 VII.8.4—5 Perturbation of infinitesimal generator of a semi-group (680—689) Peter — Weyl theorem XI.1.4 (940) Peter, F. 940 1145 Pettis, B.J. 81 83—84 88 232 235 313 387 391 473 540—541 543 Phillips' perturbation theorem VIII.1.19 (631) Phillips' perturbation theorem, Hille — Yosida — Phillips' theorem VIII.1.13 (624) Phillips, R.S. 233 234—235 373 388 390 398 395 462 463 466 541 548 553—554 612 624 726—728 729 888 1274 Phragmen, E. 1043 1115 Pick, G. 1080 Picone, M. 1588 1562 Pierce, R. 395 Pincherle, S. 80 Pinsker, A.G. 395 Pitt, H.R. 729 Plancherel theorem XI.8.9 (963) XI.3.20 Plancherel, M. 963 Plessner, A.I. 922 1269 1274 Poincare, H. 607 Pointwise ergodic theorems, k-parameter continuous case in VIII.7.17 (708) Pointwise ergodic theorems, k-parameter continuous case in VIII.7.10 (694) Pointwise ergodic theorems, k-parameter discrete case VIII.6.9 (679) Pointwise ergodic theorems, one-parameter continuous case VIII.7.5 (690) Pointwise ergodic theorems, one-parameter discrete case VIII.6.6 (675) Pointwise ergodic theorems, remarks on (729—730) Pointwise Fubini — Jessen theorem III.11.27 (209) Poisson summability IV.14.47 (363) Poisson, S.D. 863 Polar decomposition of an operator X.9 (935) Pole, of an analytic function (229) Pole, of an operator, criteria for VII.3.18 (573) VII.3.20 Pole, of an operator, definition VII.3.15 (571) Pollard, H. 728 1161 1265 Polynomial in an operator, characteristic VII.2.1 (561) VII.5.17 VII.10.8 Polynomial in an operator, in a finite dimensional space VII.1.1 (556) Polynomial in an operator, in a general space VII.3.10 (568) VII.5.17 Polynomial of an unbounded closed operator VII.9.6—10 (602—604) Pontrjagin, L. 47 79 1145 1157 1158 1160 Poole, E.G.C. 1433 1503 Positive definite operator, definition X.4.1 (906) POVZNER, A. 1587 1626 Preparation theorem of Weierstrass (232) Price, G.B. 232—233 Principal value integral, definition XI.7.1 (1050) Product, Cartesian, of measure spaces III.11 (235) Product, cartesian, of sets I.8.11 (9) Product, Cartesian, of spaces I.3 Product, Cartesian, topology I.8.1 (32) Product, Cartesian, Tychonoff theorem I.8.5 (32) Product, intersection of sets (2) Product, of B-spaces (89—90) Product, of operators (87) Product, scalar, in a Hilbert space IV.2.26 (242) Projection mapping in Cartesian products, continuity and openness I.3.3. (82) Projection mapping in Cartesian products, definition I.3.14 (9) Projection, and complements (553) Projection, and extensions (554) Projection, definition (37) VI.3.1 Projection, exercises on VI.9.16—25 (513—514) VI.9.27—29 Projection, natural order for VI.3.4 (481) Projection, orthogonal or perpendicular IV.4.8 (250) (482) Projection, study of VI.3 Proper value, definition (606) Ptak, V. 84 466 Putnam, C.R. 934 935 1563 1587 1592 1599 1600 1610 Quasi-equicontinuity, and weak compactness IV.6.14 (269) IV.6.29 Quasi-equicontinuity, for bounded functions IV.6.28 (280) Quasi-equicontinuity, for continuous functions IV.6.13 (269) Quasi-nilpotent operator, definition VII.5.12 (581) Quasi-uniform convergence, as a criterion for continuous limit IV.6.11 (268) Quasi-uniform convergence, definition IV.6.10 (268) Quasi-uniform convergence, properties IV.6.12 (269) IV.6.30—31 Quigley, F.D. 385 Quotient, group (35) see Quotient, of B-algebras IX.1 (866) Quotient, space (38) Rabinovic, Yu.L. 612 Radicals in B-algebras IX.2.5 (869) Radius, spectral VII.3.5 (567) Radon measure, definition (142) Radon — Nikodym theorem, counterexample III.13.2 (222) Radon — Nikodym theorem, for bounded additive set functions IV.9.14 (815) Radon — Nikodym theorem, general case III.10.7 (181) Radon — Nikodym theorem, positive case III.10.2 (176) Radon — Nikodym theorem, remarks on (234) Radon, J. 142 176 181—182 234 380 388 392 539 543 Raikov, D.A. 1152 1160 1274 Ramaswami, V. 884 Range of an operator VI.2.8 (479) Range of an operator, closed, criterion for VII.4.1 (577) Range of an operator, closed, criterion for, study of VI.6 VI.9.15 VI.9.17 Range of an operator, remarks on (539) Rapoport, I.M. 1587 Rasevskii, P.K. 1149 Rayleigh equation X.4 (907) Rayleigh, Lord 611 907 928 Real numbers, extended (3) Real numbers, topology (11) Real part, of a complex number (4) Real vector apace (38) (49) Rectifiable curve (225) Reflexivity, alternate proof V.7.11 (436) Reflexivity, criterion for V.4.7 (425) Reflexivity, definition II.3.22 (66) Reflexivity, discussion (88) Reflexivity, examples of reflexive space IV.15 Reflexivity, properties II.3.23—24 (67) II.8.28—29 Reflexivity, remarks on (463) (473) Regular B-space see "Reflexivity" Regular closure (462—463) Regular convexity (462—463) Regular element in a B-algebra IX.1.2 (861) Regular element in a ring (40) Regular method of summability II.4.35 (75) Regular point of a differential equation XIII.6 (1432) Regular set function see also "Set function" Regular set function, additional properties III.9.19—22 (170) Regular set function, countable additivity and regularity III.5.13 (188) Regular set function, definition III.5.11 (187) Regular set function, extension of III.5.14 (138) Regular set function, products of III.13.7 (223) Regular set function, regularity of variations III.5.12 (187) Regular set function, vector-valued measure IV.13.75 (350) Regular singularity of a differential equation XIII.6 (1432) XIII.6 Regular topological space, completely regular VI.6.21—22 (276) Regular topological space, definition I.5.1 (15) Regular topological space, normality of, with countable base (24) Reid, W.T. 938 Relative topology, definition I.4.12 (12) Rellich, F. 372 373 611—612 927 929 1263 1592 1593 1604 Representation, as a space of continuous functions IV.6.13—22 (274—276) IV.7.6 (394—397) Representation, as a space of integrable functions (394—396) Representation, for Boolean algebras (44) Representation, for Boolean rings with unit I.12.1 (41) Representation, for conjugate spaces IV.15 Representation, for unitary groups of operators XII.6.1 (1243) Representation, for vector-valued integrals III.11.17 (198) Representation, of a vector-valued function (196) Representation, of finitely additive set functions IV.9.10—11 (312) IV.9.13 Representation, of operators, in VI.8 (540—541) Representation, of operators, in C VI.7 (539—540) Representation, of operators, in other spaces (542—552) Resolution of the identity X.1 (889) Resolution of the identity, for a normal operator X.2.5 (898) Resolution of the identity, for an unbounded operator XII.2.4 (1196) Resolution of the identity, formula for X.6.1 (920) XII.2.10 Resolvent, definition VII.3.1 (566) Resolvent, equation VII.3.6 (566) Resolvent, of an element in a B-algebra IX.1.2 (861) Resolvent, set VII.3.1 (566) Resolvent, set of an element in a B-algebra IX.1.2 (861) Resolvent, study of VII.3 Rickart, C.E. 233 234 541 543 883 886 Riemann, B. 1508 1592 Riesz convexity theorem VI.10 VI.10.11 Riesz convexity theorem, applications and extensions VI.11 Riesz convexity theorem, inequality of XI.1.8 (1059) Riesz convexity theorem, remarks on (541—542) Riesz, F. 79 80—81 85—86 88 265 372—373 380 387 388 392 395 538 539 606 608 609 659 728—729 926 927 928 929 933 935 1268 1269 1272 1273 1274 Riesz, M. 388 525 532 541 1059 1164 Rinehart, R.F. 607 Ring (algebraic), Boolean (40) Ring (algebraic), definition (35) Ring (algebraic), properties (40—44) Ring (algebraic), study of I.11—12 Riss, J. 1161 Ritz, W. 928 Roberts, B.D. 93 Rogers, C.A. 93 Rohlin, V.A. 929 1269 Rosenblatt, M. 406 Rosenbloom, P.C. 47 612 Rosenfeld, N.S. 1614 1615 Rosenthal, A. 232 234—235 390 Rosser, J.B. 47—48 Rota, extension theory of XIII.10.F (1612) Rota, G.C. 1612 Rotational invariance (402—403) Rotho, E.H. 92 470 Rubin, H. 393 Rudin, W. 385 Ruston, A.F. 473 610 Rutickii, Ya.B. 400 Rutman, M. 94 395 466 Rutovitz, D. 1616 1621 Ryll-Nardzewski, C. 683 724 729 Saks decomposition, of a measure space IV.9.7 (308) Saks, S. 80 82 158 232 233—235 308 380 390 392 462 720 Salem, R. 542 San Juan, R. 387 Sargent, W.L.C. 81 400 Scalar product in a Hilbert space IV.2.26 (242) Scalars (36) Schaffer, J.J. 931 932 933 934 Schafke, F.W. 94 612 Schatten, R. 90 1163 Schauder, J. 83 84 93—94 456 470 485 539 609 Schmidt, E. 79 88 532 609 1087 1260 1269 1584 1590 Schoenberg, I.J. 380 393—394 728 1274 Schreiber, M. 932 Schreier, O. 79 462 Schroder, J. 612 Schrodinger, E. 611 1585 Schur, I. 532 Schur, J. 77 388 Schwartz, H.M. 391 Schwartz, J.T. 375 387 389 392 540 543 612 1269 1588 Schwartz, L. 82 84 399 401 402 466 611 1161 1162 1645 Schwarz inequality IV.4.1 (248) Schwarz, H.A. 248 372 Schwerdtfeger, H. 606 Sears, D.B. 1590 1591 1597 1604 1607 1616 1619 Sebastiao e Silva, J. 235 399 Segal, I.E. 384 727 928 929 1160 1161 1269 Seidel, P.L. 383 Seitz, F. 1592 Self adjoint operator X.4.1 (906) Self adjoint subspace XII.4.14 (1230) Semi-bounded operators, definition XII.5.1 (1240) Semi-group of operators, definition VIII.1.1 (614) Semi-group of operators, infinitesimal generator of VIII.1.6 (619) Semi-group of operators, k-parameter VIII.7.8 (693) Semi-group of operators, perturbation theory of (630—639) Semi-group of operators, strongly continuous (685) Semi-group of operators, strongly measurable (685) Semi-group of operators, study of VIII.1—3 Semi-simple B-algebra IX.2.5 (869) Semi-variation of a vector-valued measure, definition IV.10.3 (320) Semi-variation of a vector-valued measure, properties IV.10.4 (320) Separability and compact sets V.7.15—16 (437) Separability and compact sets, criterion for V.7.36 (438) Separability and compact sets, of C V.7.17 (437) Separability and embedding V.7.12 (436) V.7.14 Separability and metrizability V.5.1—2 (426) Separable linear manifolds II.1.5 (50) see Separable linear manifolds, in III.8.5 (168) III.9.6 Separable linear manifolds, in C IV.13.16 (340) Separable sets I.6.11 (21) see Separably-valued III.1.11 (100) Separation of convex sets, counter examples V.7.25—28 (437) Separation of convex sets, in finite dimensional spaces V.7.24 (437) Separation of convex sets, in linear spaces V.1.12 (412) Separation of convex sets, in linear topological spaces V.2.7—13 (417—418) SEQUENCE see also "Convergence" Sequence, Cauchy I.6.5 (19) Sequence, Cauchy, generalized I.7.4 (28) Sequence, Cauchy, weak II.3.25 (67) Sequence, convergent I.6.5 (19) Sequence, definitions IV.2.4—11 (239—240) IV.2.28 Sequence, definitions, properties IV. 15 Sequence, factor (366) Sequence, generalized I.7.1 (26) Sequence, generalized, generated by an ultrafilter (280) Sequence, of sets, non-increasing and limits of III.4.3 (126) Sequential compactness, definition 1.6.10 (21) Sequential compactness, relations with other compactness in metric spaces I.6.13 (21) 1.6.15 Sequential compactness, weak, definition II.3.25 (67) Sequential compactness, weak, in reflexive spaces II.3.28 (68) Sequential compactness, weak, in special spaces IV. 15 Series see also "Convergence" Series, lacunary IV.14.63 (366) Series, orthogonal IV.14 Series, summability of II.4.31—54 (74—78) Set function, III.5.7 (136) Set function, additive III.1.2 (96) Set function, bounded variation of III.1.4 (97) Set function, continuity of III.4.12 (131) III.10 Set function, convergence of III.7.2—4 (158—160) IV.9 IV.15 Set function, countable additive III.4.1 (126) Set function, countable additive, study of III.4 Set function, decomposition of III.1.8 (98) III.4.7—14 (233) Set function, definition III.1.1 (85) Set function, differentiation of III.12 Set function, extensions of III.5 Set function, extensions of, non-uniqueness of III.9.12 (169) Set function, extensions of, to a III.5 Set function, extensions of, to arbitrary sets III.1.9—10 (99—100) Set function, measure III.4.3 (126) Set function, positive III.1.1 (95)
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