基本信息 书 名 泛函分析影印版 外文书名 出版社 高等教育出版社 作 者 (美)拉克斯 原价 11.7 出版时间 2007-02 I S B N 9787040216493 套装书 否 重量 KG 装 帧 平装 版 次 1 字 数 配套资源 页 数 590 开 本 32开 内容简介 Banach空间、Hilbert空间和线性拓扑空间的基本概念和性质，线性拓扑空间中端点集的性质，有界线性算子的性质等，还包括泛函分析较深的内容：自伴算子的谱分解理论，紧算子的理论，交换Banach代数的Gelfand理论，不变子空间的理论等 目 录 Foreword 1. Linear Spaces Axioms for linear spaces-Infinite-dimensional examples-Subspace， linear span-Quotient space-Isomorphism-Convex sets-Extreme subsets 2. Linear Maps 2.1 Algebra of linear maps， Axioms for linear maps-Sums and composites-Invertible linear maps-Nullspace and range-Invariant subspaces 2.2. Index of a linear map， Degenerate maps-Pseudoinverse-IndexmProduct formula for the index-Stability of the index 3. The Hahn，Banach Theorem 3.1 The extension theorem， Positive homogeneous， subadditive functionals-Extension of linear functionals-Gauge functions of convex sets 3.2 Geometric Hahn-Banach theorem， The hyperplane separation theorem 3.3 Extensions of the Hahn-Banach theorem， The Agnew-Morse theorem-The Bohnenblust-Sobczyk-Soukhomlinov theorem 4. Applications of the Hahn-Banach theorem 4.1 Extension of positive linear functionals， 4.2 Banach limits. 4.3 Finitely additive invariant set functions， Historical note， 5. Normed Linear Spaces 5.1 Norms， Norms for quotient spaces-Complete normed linear spaces-The spaces C， B-Lp spaces and H61der's inequality-Sobolev spaces， embedding theorems-Separable spaces 5.2 Noncompactness of the unit bail， Uniform convexity-The Mazur-Ulam theorem on isometrics 5.3 Isometrics， 6. Hilbert Space 6.1 Scalar product， Schwarz inequality Parallelogram identity——Completeness，closure-e2， L 6.2 Closest point in a closed convex subset， 54Orthogonal complement of a subspace-Orthogonal decomposition 6.3 Linear functionals， The Riesz-Frechet representation theorem-Lax-Milgram lemma 6.4 Linear span， Orthogonal projection-Orthonormal bases， Gram-Schmidt process-Isometries of a Hilbert space 7. Applications of Hilbert Space Results 7.1 Radon-Nikodym theorem， 7.2 Dirichlet's problem， Use of the Riesz-Frechet theorem-Use of the Lax-Milgram theorem Use of orthogonal decomposition 8. Duals of Normed Linear Spaces
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