vmenaNZ厌匣C底、｀丿r，。x（0000B。EH1-1�/),叫一：．符号表一切，任一个存在，某一个几乎处处全体正整数全体整数全体实数n维Euclid空间全体复数数域实数或复数正无穷大或复平面上的无穷远点空集向量空间的零元素以x。为中心，以r为半径的开球集合E的内点全体对应到一对一嵌入右端是左端的定义存在唯一当且仅当蕴含证毕、述毕目录第一章度量空间................................1§1压缩映射原理............................1§2完备化.......························11§3列紧集··································15§4赋范线性空间····························234.1线性空间........·····················234.2线性空间上的距离························254.3范数与Banach空间·······················304.4赋范线性空间上的范数等价··················354.5应用：最佳逼近问题·······················394.6有穷维B*空间的刻画·····················424.7商空间································44§5凸集与不动点····························505.1定义与基本性质.....···········505.2Brouwer与Schauder不动点定理··············565.3应用·································59§6内积空间································616.1定义与基本性质......···················626.2正交与正交基···························686.3正交化与Hilbert空间的同构·················746.4再论最佳逼近问题························766.5应用：最小二乘法.....··················80第二章线性算子与线性泛函.......···············86§1线性算子的概念···························861.1线性算子和线性泛函的定义..........·····861.2线性算子的连续性和有界性··················88•11•泛函分析讲义（第二版）（上）§2Riesz表示定理及其应用····················92§3纲与开映射定理......·····1023.1纲与纲推理·····························1023.2开映射定理........··········1063.3闭图像定理·····························1123.4共鸣定理...........·················1143.5应用.........................········116§4Hahn-Banach定理......··············1224.1线性泛函的延拓定理·······················1224.2几何形式——凸集分离定理·················1304.3应用.........···············137§5共扼空间、弱收敛、自反空间...........······1455.1共辄空间的表示及应用........············1455.2共辄算子.............................·1565.3弱收敛及＊弱收敛························1625.4弱列紧性与＊弱列紧性.............······1675了弱收敛的例子............···············173§6线性算子的谱..�•............·············1796.1定义与例..........................····1796.2Gelfand定理............·············1836.3例子....................·············188第三章§1§2§3紧算子与Fredholm算子...............····193紧算子的定义和基本性质.............
