扫一扫
关注中图网
官方微博
本类五星书更多>
-
>
湖南省志(1978-2002)?铁路志
-
>
公路车宝典(ZINN的公路车维修与保养秘籍)
-
>
晶体管电路设计(下)
-
>
基于个性化设计策略的智能交通系统关键技术
-
>
德国克虏伯与晚清火:贸易与仿制模式下的技术转移
-
>
花样百出:贵州少数民族图案填色
-
>
识木:全球220种木材图鉴
公共不变子空间与紧型条件(英) 版权信息
- ISBN：9787030687128
- 条形码：9787030687128 ; 978-7-03-068712-8
- 装帧：一般胶版纸
- 册数：暂无
- 重量：暂无
- 所属分类：>
公共不变子空间与紧型条件(英) 内容简介
主要总结了算子集合的不变子空间性质，以及类紧算元的相关结果。在算子理论中，我们把紧的拟幂零算子称为Volterra算子。由Volterra算子组成的集合亦称为Volterra集合，如Volterra半群，Volterra代数等。在本书的部分，我们主要讨论Volterra半群，Volterra李代数，Volterra约当代数的不变子空间问题，这些问题都曾经是算子理论、算子李代数中的经典公开问题，在1999-2005年左右得以解决，收录于本书部分。在本书的第二部分，我们讨论了幂零李代数生成Banach代数是否为Engel代数的这一公开问题，这也是算子李代数的经典问题，至今尚未接近解决，相关部分结果收录于第五章，随后我们把紧算子的相关性质向Banach代数中类紧元集合推广，给出了离散根的定义和性质，很后，我们给出了离散根的扰动理论，这从经典的算子理论中的扰动理论刻画了离散根的本质。除本人研究成果外，本文亦收录了有名算子理论学者Shulman,Turovskii,Kennedy等专家的从1999到2019年的相关成果。
公共不变子空间与紧型条件(英) 目录
Contents
Preface
Notation
Part I Preliminaries
Chapter 1 Banach Algebras 3
1.1 Jacobson radical and derivation 3
1.2 Analytic properties of the spectrum 5
1.3 Representation theory 6
Chapter 2 Operator Theory 8
2.1 Compact operators 8
2.2 Riesz and scattered operators 10
2.3 Decomposable operator 11
Chapter 3 Lie Algebras 15
3.1 Nilpotent and solvable Lie algebras 15
3.2 Engel algebras 17
3.3 Semisimple Lie algebras 20
Part II Beger-Wang Formulas and Applications
Chapter 4 Joint Spectral Radius 23
4.1 Preliminary properties 23
4.2 Joint quasinilpotence 26
4.3 Analytic properties 29
4.4 Hausdorff measure 31
4.5 Hausdorff and essential spectral radii 32
Chapter 5 Topological Radicals 36
5.1 Preliminary properties 36
5.2 Compactly quasinilpotent radical 37
5.3 Hypocompact radical 45
5.4 The radical rad ^ Rhc 50
Chapter 6 Beger-Wang Formula and Applications 52
6.1 Compactly quasinilpotence 52
6.2 Joint spectral radius on complete chain case 58
6.3 Beger-Wang formula 60
6.4 Coincidence of Hausdorff and essential radii 70
Chapter 7 Generalized Beger-Wang Formulas and Applications 75
7.1 Mixed GBWF 75
7.2 Operator GBWF 80
7.3 Banach algebraic GBWF 81
7.4 Volterra Lie algebra problem 83
Notes 90
Part III Volterra Ideal Theorem and Applications
Chapter 8 Elementary Spectral Manifolds 95
8.1 Preliminary properties 95
8.2 Algebraic and spatial formulas 99
8.3 Applications to scattered operators 103
Chapter 9 Volterra Ideal Problem 112
9.1 A reducibility criterion 112
9.2 Quasi-commutant and quasi-center 114
9.3 Solution of Volterra ideal problem 118
Chapter 10 Lie Algebras of Compact Operators 124
10.1 Engel and E-solvable ideals 124
10.2 ad-compact element 128
10.3 Largest E-solvable ideal 130
Chapter 11 Ad-Compact Lie Algebras 136
11.1 The largest Engel ideal 136
11.2 Irreducible representations by compact operators 138
11.3 E-solvable algebras and E-radical 141
Notes 149
Part IV Lie Algebras Generated by Special Operators
Chapter 12 Essentially Nilpotent Lie Algebras 153
12.1 Two Problems on operator Lie algebras 153
12.2 Nilpotent Lie algebras generated by decomposable operators 154
12.3 Lie algebras generated by quasinilpotent operators 156
12.4 Compact quasinilpotence 159
Chapter 13 Lie Algebras Generated by Operators on Hilbert Spaces 162
13.1 Finite dimensional selfadjoint Lie algebras 162
13.2 Finite dimensional semisimple Lie algebras 166
13.3 Selfadjoint ad-compact E-solvable Lie algebras 170
Chapter 14 Lie Algebras Generated by Jordan Operators 172
14.1 Lie algebras generated by normal operators 172
14.2 Lie algebras generated by Jordan operators 175
Chapter 15 Lie Algebras Generated by Riesz Operators 180
15.1 Engel Lie algebras 180
15.2 E-solvable Lie algebras 183
15.3 Applications to polynomially compact operators 189
Notes 191
Bibliography 192
Index 195
Preface
Notation
Part I Preliminaries
Chapter 1 Banach Algebras 3
1.1 Jacobson radical and derivation 3
1.2 Analytic properties of the spectrum 5
1.3 Representation theory 6
Chapter 2 Operator Theory 8
2.1 Compact operators 8
2.2 Riesz and scattered operators 10
2.3 Decomposable operator 11
Chapter 3 Lie Algebras 15
3.1 Nilpotent and solvable Lie algebras 15
3.2 Engel algebras 17
3.3 Semisimple Lie algebras 20
Part II Beger-Wang Formulas and Applications
Chapter 4 Joint Spectral Radius 23
4.1 Preliminary properties 23
4.2 Joint quasinilpotence 26
4.3 Analytic properties 29
4.4 Hausdorff measure 31
4.5 Hausdorff and essential spectral radii 32
Chapter 5 Topological Radicals 36
5.1 Preliminary properties 36
5.2 Compactly quasinilpotent radical 37
5.3 Hypocompact radical 45
5.4 The radical rad ^ Rhc 50
Chapter 6 Beger-Wang Formula and Applications 52
6.1 Compactly quasinilpotence 52
6.2 Joint spectral radius on complete chain case 58
6.3 Beger-Wang formula 60
6.4 Coincidence of Hausdorff and essential radii 70
Chapter 7 Generalized Beger-Wang Formulas and Applications 75
7.1 Mixed GBWF 75
7.2 Operator GBWF 80
7.3 Banach algebraic GBWF 81
7.4 Volterra Lie algebra problem 83
Notes 90
Part III Volterra Ideal Theorem and Applications
Chapter 8 Elementary Spectral Manifolds 95
8.1 Preliminary properties 95
8.2 Algebraic and spatial formulas 99
8.3 Applications to scattered operators 103
Chapter 9 Volterra Ideal Problem 112
9.1 A reducibility criterion 112
9.2 Quasi-commutant and quasi-center 114
9.3 Solution of Volterra ideal problem 118
Chapter 10 Lie Algebras of Compact Operators 124
10.1 Engel and E-solvable ideals 124
10.2 ad-compact element 128
10.3 Largest E-solvable ideal 130
Chapter 11 Ad-Compact Lie Algebras 136
11.1 The largest Engel ideal 136
11.2 Irreducible representations by compact operators 138
11.3 E-solvable algebras and E-radical 141
Notes 149
Part IV Lie Algebras Generated by Special Operators
Chapter 12 Essentially Nilpotent Lie Algebras 153
12.1 Two Problems on operator Lie algebras 153
12.2 Nilpotent Lie algebras generated by decomposable operators 154
12.3 Lie algebras generated by quasinilpotent operators 156
12.4 Compact quasinilpotence 159
Chapter 13 Lie Algebras Generated by Operators on Hilbert Spaces 162
13.1 Finite dimensional selfadjoint Lie algebras 162
13.2 Finite dimensional semisimple Lie algebras 166
13.3 Selfadjoint ad-compact E-solvable Lie algebras 170
Chapter 14 Lie Algebras Generated by Jordan Operators 172
14.1 Lie algebras generated by normal operators 172
14.2 Lie algebras generated by Jordan operators 175
Chapter 15 Lie Algebras Generated by Riesz Operators 180
15.1 Engel Lie algebras 180
15.2 E-solvable Lie algebras 183
15.3 Applications to polynomially compact operators 189
Notes 191
Bibliography 192
Index 195
展开全部
公共不变子空间与紧型条件(英) 节选
Part I Preliminaries Chapter 1 Banach Algebras 1.1 Jacobson radical and derivation In this book， we assume that every vector space is over the complex field C. A complex associative algebra is a vector space A over the complex field C， with a multiplication satisfying the following properties: x(yz) = (xy)z， x(y + z) = xy + xz， (y + z)x = yx + zx， λ(xy) = (λx)y = x(λy)， for all x， y， z 2 A and λ 2 C. If moreover A is a normed space for a norm ||.|| and satisfies the norm inequality for all x， y∈A， we say that A is a normed algebra. Furthermore， If A is a Banach space， we say that A is a Banach algebra. If there is an element in A， denoted by 1， with 1x = x1 = x， for every x ∈A. Then A is called unital， and 1 is called the unit. If a normed algebra A is not unital， it is always possible to imbed it isometrically in the normed algebra with unit as in [1， Chapter III， Section 1]. In the following of this section， let A be a unital Banach algebra. For some x 2 A， if there is y∈ A， such that xy = yx = 1， then we call x is invertible in A. The set of all the invertible elements in A is denoted by G(A). Then we can define the spectrum of x in A， denoted by σA(x) (or σ(x) for brief) as follows. It is well known that σ(x) is nonempty and compact by [1， Theorem 3.2.8]. The spectral radius of x in A， denoted by ρA(x) (or ρ(x) for brief) is defined by . Then by Gelfand’s Theorem [1， Theorem 3.2.8]. If ρ(x) = 0， then x is called quasinilpotent. We also need the holomorphic functional calculus， which is also called Riesz functional calculus. One can find the information in [1， Chapter III， Section 3].
书友推荐
本类畅销
-
黑科技驱动世界的100项技术
¥21.9¥69.8 -
黑科技:驱动世界的100项技术(八品)
¥21.9¥69.8 -
指火控弹道与射击诸元理论
¥38.7¥49 -
智能照明工程手册
¥29.9¥49.8 -
光电直读光谱分析技术与应用
¥38.7¥49 -
服务型制造
¥76.3¥109
