Knowledge (XXG)

Kachurovskii's theorem

Source đź“ť

870: 340: 223: 759: 422: 585: 899: 712: 567: 256: 543: 435: 524: 415: 384: 794: 439: 590: 146: 646: 873: 595: 580: 408: 610: 855: 615: 809: 733: 850: 666: 73: 600: 894: 702: 503: 575: 799: 830: 774: 738: 109: 37: 813: 779: 717: 431: 375:. Mathematical Surveys and Monographs 49. Providence, RI: American Mathematical Society. pp.  804: 671: 784: 380: 376: 33: 789: 707: 676: 656: 641: 636: 631: 468: 368: 394: 651: 605: 553: 548: 519: 400: 391: 25: 478: 840: 692: 493: 888: 845: 769: 498: 483: 473: 369: 835: 488: 458: 29: 764: 754: 661: 463: 17: 371:
Monotone operators in Banach space and nonlinear partial differential equations
697: 537: 533: 529: 53: 335:{\displaystyle {\big (}\mathrm {d} f(x)-\mathrm {d} f(y){\big )}(x-y)\geq 0.} 354:
Kachurovskii, R. I. (1960). "On monotone operators and convex functionals".
404: 259: 149: 235:
is an (increasing) monotone operator, i.e., for all
218:{\displaystyle \mathrm {d} f(x)(y-x)\leq f(y)-f(x);} 823: 747: 726: 685: 624: 566: 512: 447: 760:Spectral theory of ordinary differential equations 334: 217: 76:that is FrĂ©chet differentiable with derivative d 416: 306: 262: 8: 451: 423: 409: 401: 305: 304: 287: 267: 261: 260: 258: 150: 148: 713:Group algebra of a locally compact group 115:.) Then the following are equivalent: 7: 72: ∪ {+∞} be an 288: 268: 151: 14: 869: 868: 795:Topological quantum field theory 900:Theorems in functional analysis 323: 311: 301: 295: 281: 275: 209: 203: 194: 188: 179: 167: 164: 158: 1: 591:Uniform boundedness principle 74:extended real-valued function 367:Showalter, Ralph E. (1997). 916: 734:Invariant subspace problem 24:is a theorem relating the 864: 454: 703:Spectrum of a C*-algebra 44:Statement of the theorem 800:Noncommutative geometry 108:) is an element of the 856:Tomita–Takesaki theory 831:Approximation property 775:Calculus of variations 336: 219: 22:Kachurovskii's theorem 851:Banach–Mazur distance 814:Generalized functions 337: 220: 122:is a convex function; 110:continuous dual space 596:Kakutani fixed-point 581:Riesz representation 257: 147: 780:Functional calculus 739:Mahler's conjecture 718:Von Neumann algebra 432:Functional analysis 88: →  68: →  28:of a function on a 805:Riemann hypothesis 504:Topological vector 332: 215: 56:of a Banach space 38:FrĂ©chet derivative 882: 881: 785:Integral operator 562: 561: 397:(Proposition 7.4) 356:Uspekhi Mat. Nauk 907: 872: 871: 790:Jones polynomial 708:Operator algebra 452: 425: 418: 411: 402: 390: 374: 363: 341: 339: 338: 333: 310: 309: 291: 271: 266: 265: 224: 222: 221: 216: 154: 915: 914: 910: 909: 908: 906: 905: 904: 895:Convex analysis 885: 884: 883: 878: 860: 824:Advanced topics 819: 743: 722: 681: 647:Hilbert–Schmidt 620: 611:Gelfand–Naimark 558: 508: 443: 429: 387: 366: 353: 350: 255: 254: 145: 144: 46: 12: 11: 5: 913: 911: 903: 902: 897: 887: 886: 880: 879: 877: 876: 865: 862: 861: 859: 858: 853: 848: 843: 841:Choquet theory 838: 833: 827: 825: 821: 820: 818: 817: 807: 802: 797: 792: 787: 782: 777: 772: 767: 762: 757: 751: 749: 745: 744: 742: 741: 736: 730: 728: 724: 723: 721: 720: 715: 710: 705: 700: 695: 693:Banach algebra 689: 687: 683: 682: 680: 679: 674: 669: 664: 659: 654: 649: 644: 639: 634: 628: 626: 622: 621: 619: 618: 616:Banach–Alaoglu 613: 608: 603: 598: 593: 588: 583: 578: 572: 570: 564: 563: 560: 559: 557: 556: 551: 546: 544:Locally convex 541: 527: 522: 516: 514: 510: 509: 507: 506: 501: 496: 491: 486: 481: 476: 471: 466: 461: 455: 449: 445: 444: 430: 428: 427: 420: 413: 405: 399: 398: 385: 364: 349: 346: 345: 344: 343: 342: 331: 328: 325: 322: 319: 316: 313: 308: 303: 300: 297: 294: 290: 286: 283: 280: 277: 274: 270: 264: 249: 248: 228: 227: 226: 225: 214: 211: 208: 205: 202: 199: 196: 193: 190: 187: 184: 181: 178: 175: 172: 169: 166: 163: 160: 157: 153: 139: 138: 123: 92:at each point 84:) :  45: 42: 13: 10: 9: 6: 4: 3: 2: 912: 901: 898: 896: 893: 892: 890: 875: 867: 866: 863: 857: 854: 852: 849: 847: 846:Weak topology 844: 842: 839: 837: 834: 832: 829: 828: 826: 822: 815: 811: 808: 806: 803: 801: 798: 796: 793: 791: 788: 786: 783: 781: 778: 776: 773: 771: 770:Index theorem 768: 766: 763: 761: 758: 756: 753: 752: 750: 746: 740: 737: 735: 732: 731: 729: 727:Open problems 725: 719: 716: 714: 711: 709: 706: 704: 701: 699: 696: 694: 691: 690: 688: 684: 678: 675: 673: 670: 668: 665: 663: 660: 658: 655: 653: 650: 648: 645: 643: 640: 638: 635: 633: 630: 629: 627: 623: 617: 614: 612: 609: 607: 604: 602: 599: 597: 594: 592: 589: 587: 584: 582: 579: 577: 574: 573: 571: 569: 565: 555: 552: 550: 547: 545: 542: 539: 535: 531: 528: 526: 523: 521: 518: 517: 515: 511: 505: 502: 500: 497: 495: 492: 490: 487: 485: 482: 480: 477: 475: 472: 470: 467: 465: 462: 460: 457: 456: 453: 450: 446: 441: 437: 433: 426: 421: 419: 414: 412: 407: 406: 403: 396: 393: 388: 386:0-8218-0500-2 382: 378: 373: 372: 365: 362:(4): 213–215. 361: 357: 352: 351: 347: 329: 326: 320: 317: 314: 298: 292: 284: 278: 272: 253: 252: 251: 250: 246: 242: 238: 234: 230: 229: 212: 206: 200: 197: 191: 185: 182: 176: 173: 170: 161: 155: 143: 142: 141: 140: 136: 132: 128: 124: 121: 118: 117: 116: 114: 111: 107: 103: 100:. (In fact, d 99: 95: 91: 87: 83: 79: 75: 71: 67: 64: :  63: 59: 55: 54:convex subset 51: 43: 41: 39: 35: 31: 27: 23: 19: 836:Balanced set 810:Distribution 748:Applications 601:Krein–Milman 586:Closed graph 370: 359: 355: 244: 240: 236: 232: 134: 130: 126: 119: 112: 105: 101: 97: 93: 89: 85: 81: 77: 69: 65: 61: 57: 49: 47: 34:monotonicity 30:Banach space 21: 15: 765:Heat kernel 755:Hardy space 662:Trace class 576:Hahn–Banach 538:Topological 18:mathematics 889:Categories 698:C*-algebra 513:Properties 348:References 672:Unbounded 667:Transpose 625:Operators 554:Separable 549:Reflexive 534:Algebraic 520:Barrelled 327:≥ 318:− 285:− 198:− 183:≤ 174:− 26:convexity 874:Category 686:Algebras 568:Theorems 525:Complete 494:Schwartz 440:glossary 125:for all 60:and let 677:Unitary 657:Nuclear 642:Compact 637:Bounded 632:Adjoint 606:Min–max 499:Sobolev 484:Nuclear 474:Hilbert 469:FrĂ©chet 434: ( 395:1422252 36:of its 32:to the 652:Normal 489:Orlicz 479:Hölder 459:Banach 448:Spaces 436:topics 383:  464:Besov 52:be a 812:(or 530:Dual 381:ISBN 239:and 129:and 48:Let 243:in 133:in 96:in 16:In 891:: 438:– 392:MR 379:. 377:80 360:15 358:. 330:0. 40:. 20:, 816:) 540:) 536:/ 532:( 442:) 424:e 417:t 410:v 389:. 324:) 321:y 315:x 312:( 307:) 302:) 299:y 296:( 293:f 289:d 282:) 279:x 276:( 273:f 269:d 263:( 247:, 245:K 241:y 237:x 233:f 231:d 213:; 210:) 207:x 204:( 201:f 195:) 192:y 189:( 186:f 180:) 177:x 171:y 168:( 165:) 162:x 159:( 156:f 152:d 137:, 135:K 131:y 127:x 120:f 113:V 106:x 104:( 102:f 98:K 94:x 90:R 86:V 82:x 80:( 78:f 70:R 66:K 62:f 58:V 50:K

Index

mathematics
convexity
Banach space
monotonicity
Fréchet derivative
convex subset
extended real-valued function
continuous dual space
Monotone operators in Banach space and nonlinear partial differential equations
80
ISBN
0-8218-0500-2
MR
1422252
v
t
e
Functional analysis
topics
glossary
Banach
Besov
Fréchet
Hilbert
Hölder
Nuclear
Orlicz
Schwartz
Sobolev
Topological vector

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

↑