Morita系统环上的可加映射 英文PDF电子书下载

本书第一章：序言，包括研究背景及本书主要内容。第二章：Morita系统环的定义及例子。第三章：Morita系统环上的线性映射。内容包括交换映射、李型导子、约当导子等。第四章：Morita系统环上的非线性映射和高阶映射。内容包括约当高阶导子、非线性李高阶导子、非线性约当同态等。第五章：线性映射的局部刻画。包括在零点可导的映射、在幂等元处可导的映射等。

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1 Definitions and Examples of Morita Context Rings 1

1.1 Definitions of Morita context rings 1

1.2 Classical matrix algebras 7

1.2.1 Full matrix algebras 7

1.2.2 Triangular matrix algebras 7

1.2.3 Block upper triangular matrix algebras 8

1.2.4 Inflated algebras 9

1.3 Quasi-hereditary algebras 10

1.3.1 Basic construction 10

1.3.2 Dual extension algebras 11

1.4 Two non-degenerate examples 14

1.4.1 Morita context rings from smash product 14

1.4.2 Morita context rings from group algebras 15

1.5 Examples of operator algebras 17

1.5.1 Triangular Banach algebras 17

1.5.2 Nest algebras 17

1.5.3 von Neumann algebras 19

1.5.4 Incidence algebras 20

2 Linear Mappings on Morita Context Rings 23

2.1 Commuting mappings on Morita context rings 23

2.1.1 Posner Theorem 25

2.1.2 Commuting mappings and centralizing mappings 28

2.1.3 Skew commuting and skew centralizing mappings 49

2.2 Lie derivations on Morita context rings 62

2.3 Jordan derivations on Morita context rings 71

2.4 Jordan generalized derivations on triangular algebras 85

2.5 Lie triple derivations on triangular algebras 94

2.5.1 Proof of the main Theorem 95

2.5.2 Another look to Theorem 2.5.1 99

2.6 Local actions of linear mappings on Morita context rings 104

3 Non-linear Mappings and Higher Mappings 111

3.1 Characterization of Jordan higher derivations 111

3.2 Jordan higher derivations on some operator algebras 118

3.3 Jordan higher derivations on triangular algebras 123

3.4 When a higher derivation is inner 136

3.5 Non-linear Lie higher derivations 147

3.6 Non linear Jordan bijective mappings 163

3.7 Jordan higher derivable points 178

Bibliography 181

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