- 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)/国外优秀数学著作原版系列/他山之石系列
- - 作者：(澳)努鲁拉·阿宰木|责编:李鹏//李兰静
  - 出版社：哈尔滨工业大学
  - ISBN：9787560394244
  - 出版日期：2021/06/01
  - 页数：202
- 售价：39.2

内容大纲
本书给出了半有限Von Neumann代数中的谱位移函数的统一阐述，以及许多其他相关的理论。这些内容包括Brown测度、Fuglede-Kadison行列式、二重算子积分、谱平均和Breuer相对Fredholm算子理论，书中还专门讨论了半有限Dixmier迹。本书共分四章，第一章为预备知识，包括希尔伯特空间中的运算符、Frechet衍生；第二章包括谱理论跟踪、谱理论痕迹的Lidski公式；第三章介绍了谱函数，包括跟踪类扰动的SSF、多重积分算子；第四章介绍了光谱流，包括初步的结果和谱移函数。本书适合对函数分析、算子理论、算子代数和数学物理等方向有兴趣的学者和专家参考阅读。
作者介绍
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

    3.1.2  The Krein trace formula: general case
  3.2  Multiple operator integrals in yon Neumann algebras
    3.2.1  BS representations
    3.2.2  Multiple operator integrals
  3.3  Higher order Frechet differenTiabiLity
  3.4  Spectral shift and spectral averaging in semifinite yon Neumann algebras
4  Spectral shift function and spectral flow
  4.1  Prelinfinary results
    4.1.1  Self-adjoint operators with T-compact resolvent
    4.1.2  Difference quotients and double operator integrals
    4.1.3  Some continuity and differentinbfiity properties of operator functions138
    4.1.4  A class Fa,b(N1, T) of T-Fredholm operators
  4.2  The  spectral  shift  function  for  operators  with  compact  resolvent
    4.2.1  The unbounded case
    4.2.2  The bounded case
  4.3  Spectral flow
    4.3.1  The spectral flow function
    4.3.2  Spectral flow one-forms: unbounded case
    4.3.3  Spectral flow one-forms: bounded case
    4.3.4  The first formula for spectral flow
    4.3.5  Spectral flow in the unbounded case
    4.3.6  The spectral flow formulae in the Z-summable spectral triple case
    4.3.7  Recovering n-invariants
Concluding remarks
Bibliography
Index
编辑手记

内容大纲

作者介绍

目录

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