作品介绍

谱理论简明教程


作者:艾文森     整理日期:2017-02-24 16:42:55


  《谱理论简明教程(英文版)》以作者提供的具备测度论和基础泛函分析的一二年级研究生十五周课程为基础,为了计算无限维空间中特殊算子谱,特别是Hilbert空间中的算子,书中在算子理论基本问题的内容框架内讲述了现代分析的基本工具。工具众多,提供了解决超越谱计算之外问题的更加具体方法的基础,这些问题如量子物理数学基础,非交换K理论,简单C*代数的分类。目次:谱理论和Banach代数;Hilbert空间上的算子;渐进:紧扰动和Fredholm理论;方法和应用。

目录
  PrefaceChapter 1. Spectral Theory and Banach Algebras 1.1. Origins of Spectral Theory 1.2. The Spectrum of an Operator 1.3. Banach Algebras: Examples 1.4. The Regular Representation 1.5. The General Linear Group of A 1.6. Spectrum of an Element of a Banach Algebra 1.7. Spectral Radius 1.8. Ideals and Quotients 1.9. Commutative Banach Algebras 1.10. Examples: C(X) and the Wiener Algebra 1.11. Spectral Permanence Theorem 1.12. Brief on the Analytic Functional CalculusChapter 2. Operators on Hilbert Space 2.1. Operators and Their C*-Algebras 2.2. Commutative C*-Algebras 2.3. Continuous Functions of Normal Operators 2.4. The Spectral Theorem and Diagonalization 2.5. Representations of Banach *-Algebras 2.6. Borel Functions of Normal Operators 2.7. Spectral Measures 2.8. Compact Operators 2.9. Adjoining a Unit to a C*-Algebra 2.10. Quotients of C*-AlgebrasChapter 3. Asymptotics: Compact Perturbations and Fredholm Theory 3.1. The Calkin Algebra 3.2. Riesz Theory of Compact Operators 3.3. Fredholm Operators 3.4. The Fredholm IndexChapter 4. Methods and Applications 4.1. Maximal Abelian yon Neumann Algebras 4.2. Toeplitz Matrices and Toeplitz Operators 4.3. The Toeplitz C*-Algebra 4.4. Index Theorem for Continuous Symbols 4.5. Some H2 Function Theory 4.6. Spectra of Toeplitz Operators with Continuous Symbol 4.7. States and the GNS Construction 4.8. Existence of States: The Gelfand-Naimark TheoremBibliographyIndex
  PrefaceChapter 1. Spectral Theory and Banach Algebras 1.1. Origins of Spectral Theory 1.2. The Spectrum of an Operator 1.3. Banach Algebras: Examples 1.4. The Regular Representation 1.5. The General Linear Group of A 1.6. Spectrum of an Element of a Banach Algebra 1.7. Spectral Radius 1.8. Ideals and Quotients 1.9. Commutative Banach Algebras 1.10. Examples: C(X) and the Wiener Algebra 1.11. Spectral Permanence Theorem 1.12. Brief on the Analytic Functional CalculusChapter 2. Operators on Hilbert Space 2.1. Operators and Their C*-Algebras 2.2. Commutative C*-Algebras 2.3. Continuous Functions of Normal Operators 2.4. The Spectral Theorem and Diagonalization 2.5. Representations of Banach *-Algebras 2.6. Borel Functions of Normal Operators 2.7. Spectral Measures 2.8. Compact Operators 2.9. Adjoining a Unit to a C*-Algebra 2.10. Quotients of C*-AlgebrasChapter 3. Asymptotics: Compact Perturbations and Fredholm Theory 3.1. The Calkin Algebra 3.2. Riesz Theory of Compact Operators 3.3. Fredholm Operators 3.4. The Fredholm IndexChapter 4. Methods and Applications 4.1. Maximal Abelian yon Neumann Algebras 4.2. Toeplitz Matrices and Toeplitz Operators 4.3. The Toeplitz C*-Algebra 4.4. Index Theorem for Continuous Symbols 4.5. Some H2 Function Theory 4.6. Spectra of Toeplitz Operators with Continuous Symbol 4.7. States and the GNS Construction 4.8. Existence of States: The Gelfand-Naimark TheoremBibliographyIndex

八字精批2025运势命中贵人八字合婚



闂佸吋鐪归崕鎻掞耿閻楀牏鈻曢柨鏃囨硶閻熸繈鏌ら搹顐㈢亰缂佹鎳忓ḿ顏堝棘閵堝洨顦柣鐘叉搐閸㈠弶绂嶉弴鐔衡攳闁斥晛鍟ˉ鍥煙鐠囪尙绠扮憸鏉挎啞缁嬪鈧綆鍙庡ḿ鈥趁瑰⿰鍐伇婵烇綆鍣i幆宥夋晸閿燂拷
闂佺ǹ绻楀▍鏇㈠极閻愬搫绀傛い鎴f硶閼稿綊鏌涘▎蹇曟闁逞屽墯缁矂宕洪崱娑欌挃妞ゎ偒鍘兼慨娑樜涢敐鍡欐喛闁逞屽墾閹凤拷,婵炴垶妫戠粻鎴濐嚕閸濄儰鐒婇柛鈩冪懅閼稿爼鏌熼鍝勫闁搞劌瀛╃粋宥夘敃閿濆棙瀚虫繛鎴炴鐠愮喖鍩€椤掑﹥瀚�
闂佸吋鐪归崕鎵箔閸涱喗濮滈柦妯侯槸缁斿墽绱撻崒妤佹珔閻庡灚锕㈠鍨緞婵犲嫭顫氶梺娲诲枙缁躲倗妲愬┑瀣Е閻忕偛澧芥竟澶愭煙濞堝灝浜為柣鏍ㄧ矒瀹曟鎼归锝嗘畼闂佹寧绋戦懟顖毭洪弽銊ョ窞鐎广儰璁查崑鎾斥堪閸犵増甯″畷銏⑩偓锝庝簽濡叉洟鏌i鏄忣唹闁逞屽墯缁诲倸鐣甸崱娑樼煑妞ゆ牗菤閸嬫捇鏁撻敓锟�

上一本:微分几何基础 下一本:当代数学史话

作家文集