Morita系统环上的可加映射 英文PDF|Epub|txt|kindle电子书版本网盘下载

Morita系统环上的可加映射 英文PDF格式电子书版下载

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1 Definitions and Examples of Morita Context Rings1

1.1 Definitions of Morita context rings1

1.2 Classical matrix algebras7

1.2.1 Full matrix algebras7

1.2.2 Triangular matrix algebras7

1.2.3 Block upper triangular matrix algebras8

1.2.4 Inflated algebras9

1.3 Quasi-hereditary algebras10

1.3.1 Basic construction10

1.3.2 Dual extension algebras11

1.4 Two non-degenerate examples14

1.4.1 Morita context rings from smash product14

1.4.2 Morita context rings from group algebras15

1.5 Examples of operator algebras17

1.5.1 Triangular Banach algebras17

1.5.2 Nest algebras17

1.5.3 von Neumann algebras19

1.5.4 Incidence algebras20

2 Linear Mappings on Morita Context Rings23

2.1 Commuting mappings on Morita context rings23

2.1.1 Posner Theorem25

2.1.2 Commuting mappings and centralizing mappings28

2.1.3 Skew commuting and skew centralizing mappings49

2.2 Lie derivations on Morita context rings62

2.3 Jordan derivations on Morita context rings71

2.4 Jordan generalized derivations on triangular algebras85

2.5 Lie triple derivations on triangular algebras94

2.5.1 Proof of the main Theorem95

2.5.2 Another look to Theorem 2.5.199

2.6 Local actions of linear mappings on Morita context rings104

3 Non-linear Mappings and Higher Mappings111

3.1 Characterization of Jordan higher derivations111

3.2 Jordan higher derivations on some operator algebras118

3.3 Jordan higher derivations on triangular algebras123

3.4 When a higher derivation is inner136

3.5 Non-linear Lie higher derivations147

3.6 Non linear Jordan bijective mappings163

3.7 Jordan higher derivable points178

Bibliography181