作者：[澳]努鲁拉.阿宰木
页数：202
出版社：哈尔滨工业大学出版社
出版日期：2021
ISBN：9787560394244
电子书格式：PDF
PDF下载地址
内容简介
《冯·诺依曼代数中的谱位移函数：半有限冯·诺依曼代数中的谱位移函数与谱流（英文）》是一部引进版权的英文版数学专著，中文书名或可译为《冯，诺依曼代数中的谱位移函数：半有限冯·诺依曼代数中的谱位移函数与谱流》。
Lifshits-Krein谱位移函数与谱流在数学分析中有着经典和完善的标记，但是多年来这些理论都是独立发展的。
《冯·诺依曼代数中的谱位移函数：半有限冯·诺依曼代数中的谱位移函数与谱流（英文）》给出了半有限冯·诺依曼代数中谱位移函数与谱流的统一解释，并且给出了这些解释所必需的一些其他课题。这些课题包括Brown测度，Fuglede-Kadison行列式，双重算子与多重算子积分，谱平均与Breuer相对Fredholm算子理论，另外，书中还用一章的内容讨论了半有限Dixmier迹，《冯·诺依曼代数中的谱位移函数：半有限冯·诺依曼代数中的谱位移函数与谱流（英文）》面向泛函分析，算子理论，算子代数与数学物理方向的学者。
目录
Introduction
1 Preliminaries
1.1 Operators in Hilbert space
1.1.1 Notation
1.1.2 Topologies of B(H)
1.1.3 Self-adjoint operators
1.1.4 Numerical range
1.1.5 The Bochner integral
1.2 Frechet derivativc
1.3 von Neumann algebras
1.3.1 Basic properties of von Neumann algebras
1.3.2 Projections in von Neumann algebras
1.3.3 Semifinite von Neumann algebras
1.3.4 Operators affiliated with a von Neumann algebra
1.3.5 Generalized s-numbers
1.3.6 Non-commutative L-spaces
1.3.7 Holomorphic functional calculus
1.3.8 Invariant operator ideals in semifinite von Neumann algebras
1.4 Integration of operator-valued functions
1.5 Theory of i-Fredhalm operators
1.5.1 Definition and elementary properties of T-Fredholm operators
1.5.2 The semifinite Fredholm alternative
1.5.3 The semifinite Atkinson theorem
1.5.4 Properties of T–Fredholm operators
1.5.5 Skew-corner T-Fredholrn operators
1,5.6 Essential codimension of two projections
1.5.7 The Carey-Phillips theorem
1.6 Spectral flow in semifinite von Neumann algebras
1.7 Fuglede-Kadison’s determinant in sernifinite yon Neumann algebras
1.7.1 de la Harpe-Seandalis determinant
1.7.2 Technical lemmas
1.7.3 Definition of Fuglede-Kadison determinant and its properties
1.8 The Brown measure
1.8.1 Weyl functions
1.8.2 The Weierstrass function
1.8.3 Subharmonic functions
1.8.4 Technical results
1.8.5 The Brown measure
1.8.6 The Lidskii theorem for the Brown measure
1.8.7 Additional properties of the Brown measure
2 Spectrality of Dixmier trace
2.1 The Dixmier trace in sermifinite yon Neumann algebras
2.1.1 The Dixmier traces in semifinite von Neumann algebras
2.1.2 Measurability of operators
2.2 Lidskii formula for Dixmier traces
2.2.1 Spectral characterization of sums of commutators
2 2.2 The Lidskii formula for the Dixmier trace
3 Spectral shift function in yon Neumann algebras
3.1 Spectral shift function for trace class perturbations
3.1.1 Krein’s trace formula: resolvent perturbations
1 Preliminaries
1.1 Operators in Hilbert space
1.1.1 Notation
1.1.2 Topologies of B(H)
1.1.3 Self-adjoint operators
1.1.4 Numerical range
1.1.5 The Bochner integral
1.2 Frechet derivativc
1.3 von Neumann algebras
1.3.1 Basic properties of von Neumann algebras
1.3.2 Projections in von Neumann algebras
1.3.3 Semifinite von Neumann algebras
1.3.4 Operators affiliated with a von Neumann algebra
1.3.5 Generalized s-numbers
1.3.6 Non-commutative L-spaces
1.3.7 Holomorphic functional calculus
1.3.8 Invariant operator ideals in semifinite von Neumann algebras
1.4 Integration of operator-valued functions
1.5 Theory of i-Fredhalm operators
1.5.1 Definition and elementary properties of T-Fredholm operators
1.5.2 The semifinite Fredholm alternative
1.5.3 The semifinite Atkinson theorem
1.5.4 Properties of T–Fredholm operators
1.5.5 Skew-corner T-Fredholrn operators
1,5.6 Essential codimension of two projections
1.5.7 The Carey-Phillips theorem
1.6 Spectral flow in semifinite von Neumann algebras
1.7 Fuglede-Kadison’s determinant in sernifinite yon Neumann algebras
1.7.1 de la Harpe-Seandalis determinant
1.7.2 Technical lemmas
1.7.3 Definition of Fuglede-Kadison determinant and its properties
1.8 The Brown measure
1.8.1 Weyl functions
1.8.2 The Weierstrass function
1.8.3 Subharmonic functions
1.8.4 Technical results
1.8.5 The Brown measure
1.8.6 The Lidskii theorem for the Brown measure
1.8.7 Additional properties of the Brown measure
2 Spectrality of Dixmier trace
2.1 The Dixmier trace in sermifinite yon Neumann algebras
2.1.1 The Dixmier traces in semifinite von Neumann algebras
2.1.2 Measurability of operators
2.2 Lidskii formula for Dixmier traces
2.2.1 Spectral characterization of sums of commutators
2 2.2 The Lidskii formula for the Dixmier trace
3 Spectral shift function in yon Neumann algebras
3.1 Spectral shift function for trace class perturbations
3.1.1 Krein’s trace formula: resolvent perturbations