Handbook of the Geometry of Banach Spaces, Volumes 1-2William B. Johnson, Joram Lindenstrauss The Handbook presents an overview of most aspects of modern Banach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banach space theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory. |
Contents
V | 1009 |
VII | 1012 |
VIII | 1013 |
IX | 1016 |
X | 1018 |
XI | 1019 |
XII | 1020 |
XIII | 1021 |
CXVI | 1397 |
CXVII | 1404 |
CXVIII | 1408 |
CXIX | 1419 |
1425 | |
CXXI | 1427 |
CXXII | 1432 |
CXXIII | 1433 |
XIV | 1028 |
XV | 1034 |
XVI | 1037 |
XVII | 1043 |
XVIII | 1045 |
XIX | 1048 |
XXI | 1051 |
XXIII | 1053 |
XXIV | 1055 |
XXV | 1060 |
XXVI | 1061 |
XXVII | 1064 |
XXVIII | 1065 |
1071 | |
XXX | 1073 |
XXXI | 1074 |
XXXII | 1076 |
XXXIII | 1081 |
XXXIV | 1089 |
XXXV | 1096 |
1099 | |
XXXVII | 1101 |
XXXIX | 1103 |
XL | 1107 |
XLI | 1111 |
XLII | 1113 |
XLIII | 1116 |
XLIV | 1119 |
XLV | 1123 |
XLVI | 1127 |
1131 | |
XLIX | 1133 |
LI | 1135 |
LII | 1138 |
LIII | 1141 |
LIV | 1144 |
LV | 1154 |
LVI | 1155 |
LVII | 1157 |
LVIII | 1158 |
LIX | 1161 |
LX | 1167 |
LXI | 1172 |
1177 | |
LXIV | 1179 |
LXV | 1180 |
LXVI | 1188 |
LXVII | 1192 |
LXVIII | 1198 |
1201 | |
LXX | 1203 |
LXXI | 1204 |
LXXII | 1208 |
LXXIII | 1212 |
LXXIV | 1216 |
LXXV | 1220 |
LXXVI | 1224 |
LXXVII | 1230 |
LXXVIII | 1234 |
LXXIX | 1240 |
LXXX | 1243 |
LXXXI | 1244 |
1247 | |
LXXXIV | 1249 |
LXXXV | 1254 |
LXXXVI | 1255 |
LXXXVII | 1257 |
LXXXVIII | 1260 |
LXXXIX | 1263 |
XC | 1266 |
XCI | 1268 |
XCII | 1278 |
XCIII | 1280 |
XCIV | 1283 |
XCV | 1291 |
XCVI | 1295 |
1299 | |
XCVIII | 1301 |
XCIX | 1306 |
C | 1307 |
CI | 1310 |
CII | 1315 |
CIII | 1320 |
CIV | 1330 |
1333 | |
CVI | 1335 |
CVII | 1352 |
CVIII | 1359 |
1361 | |
CX | 1363 |
CXI | 1364 |
CXII | 1367 |
CXIII | 1372 |
CXIV | 1377 |
CXV | 1393 |
CXXIV | 1434 |
CXXV | 1436 |
CXXVI | 1438 |
CXXVII | 1440 |
CXXVIII | 1443 |
CXXIX | 1445 |
CXXX | 1447 |
CXXXI | 1449 |
CXXXII | 1451 |
CXXXIII | 1452 |
CXXXIV | 1455 |
1459 | |
CXXXVI | 1461 |
CXXXVII | 1463 |
CXXXVIII | 1466 |
CXXXIX | 1470 |
CXL | 1477 |
CXLI | 1479 |
CXLII | 1484 |
CXLIII | 1490 |
CXLIV | 1495 |
CXLV | 1500 |
CXLVI | 1506 |
CXLVII | 1510 |
1519 | |
CXLIX | 1522 |
CLI | 1523 |
CLII | 1525 |
CLIV | 1528 |
CLVI | 1531 |
CLVII | 1535 |
CLIX | 1539 |
CLX | 1544 |
1547 | |
CLXII | 1549 |
CLXIII | 1551 |
CLXIV | 1569 |
CLXV | 1579 |
CLXVI | 1593 |
CLXVII | 1600 |
1603 | |
CLXIX | 1605 |
CLXX | 1606 |
CLXXI | 1610 |
CLXXII | 1614 |
CLXXIII | 1619 |
CLXXIV | 1624 |
CLXXV | 1625 |
CLXXVII | 1627 |
CLXXVIII | 1631 |
CLXXIX | 1632 |
1635 | |
CLXXXI | 1637 |
CLXXXIII | 1641 |
CLXXXIV | 1644 |
CLXXXV | 1651 |
CLXXXVI | 1658 |
CLXXXVII | 1665 |
CLXXXVIII | 1667 |
1671 | |
CXC | 1673 |
CXCII | 1677 |
CXCIII | 1680 |
CXCV | 1683 |
CXCVI | 1684 |
CXCVII | 1696 |
CXCVIII | 1699 |
CXCIX | 1700 |
1703 | |
CCI | 1705 |
CCII | 1716 |
CCIII | 1723 |
CCIV | 1726 |
CCV | 1729 |
CCVI | 1735 |
CCVII | 1739 |
1743 | |
CCIX | 1745 |
CCX | 1746 |
CCXI | 1760 |
CCXII | 1765 |
CCXIII | 1773 |
CCXIV | 1777 |
CCXV | 1782 |
CCXVI | 1794 |
CCXVII | 1799 |
CCXVIII | 1805 |
1806 | |
CCXX | 1817 |
1819 | |
CCXXIII | 1821 |
CCXXIV | 1823 |
1825 | |
1849 | |
Common terms and phrases
admits Amer assume asymptotic Banach space basic sequence block basis Borel bounded linear C*-algebra compact operators compact space complemented subspace complete complex interpolation constant construction contains converges convex COROLLARY cotype countable defined denote dual embedding example exists extension finite finite-dimensional Fréchet differentiable function space Gâteaux differentiable Gaussian H₁ Hence Hilbert space homeomorphic implies inequality infinite integer isometric isomorphic Lemma Lindenstrauss Lipschitz measure metric space Neumann algebra operator spaces Pełczyński Pisier pointwise problem projection proof of Theorem Proposition proved quasi-Banach space quotient reflexive resp result satisfies Section separable Banach space Sobolev spaces spreading model Studia Math subset subspace symmetric unconditional basis uniformly unique unit vector basis von Neumann algebra W.B. Johnson weak star topology weak topology weakly compact weakly null