应用泛函分析修订版(前三章)new

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1、非数学类研究生用书AppliedFunctionalAnalysis应应应用用用泛泛泛函函函分分分析析析天津大学数学系编2013年10月10日目录第一章线性空间与内积空间































1§1.1集合与映射···············································1§1.1.1集合及性质·································································1§1

2、.1.2集合的运算·································································2§1.1.3映射·········································································4§1.2集合的基数···············································5§1.2.1可数集与不可数集··························

3、·······························5§1.2.2实数集的确界存在原理···················································6§1.3线性空间与线性算子········································8§1.3.1线性空间····································································8§1.3.2线性子空间··········

4、·······················································10§1.3.3线性空间的基与维数······················································12§1.3.4线性算子····································································13§1.3.5线性同构····································

5、································14§1.4内积空间·················································15§1.4.1内积空间的定义及例······················································15§1.4.2内积空间的几何···························································16§1.4.3内积空间的线性子空间

6、与同构···········································19§1.4.4内积空间中的正交系······················································19§1.5习题一···················································22第二章赋范线性空间与度量空间




























25§2.1赋范线性空间····················

7、··························25§2.1.1赋范线性空间的定义及例子··············································25§2.1.2由范数导出的度量·························································28i§2.1.3收敛序列,连续映射·······················································29§2.1.4完备的赋范线性空

8、间······················································31§2.1.5级数与Schauder基·························································36§2.1.6子空间······································································39§2.2赋范线