| Acknowledgement | 第1-7页 |
| Abstract | 第7-8页 |
| 1 Introduction | 第8-13页 |
| ·Introduction | 第8-11页 |
| ·Preliminaries and notation | 第11-13页 |
| 2 Characterizations of Derivations on Some Operator Algebras | 第13-19页 |
| 3 Characterizations of Derivations on B(H) | 第19-25页 |
| 4 Generalized Jordan Derivations on Prime Rings and Standard Operator Algebras | 第25-34页 |
| ·Introduction | 第25-26页 |
| ·Generalized Jordan derivations on prime rings | 第26-29页 |
| ·Generalized Jordan triple derivations on prime rings | 第29-31页 |
| ·Generalized Jordan derivations on standard operator algebras | 第31-34页 |
| 5 Topological Reflexivity of The Spaces of(α,β)-derivations on Operator Algebras | 第34-46页 |
| ·Introduction and preliminaries | 第34-36页 |
| ·Topological reflexivity of the spaces of (α,β)-derivations of operator algebras | 第36-43页 |
| ·Automorphisms and (α,β)-derivations of reflexive algebras | 第43-46页 |
| 6 Additive Mappings That Preserves Rank One Nilpotent Operators | 第46-61页 |
| ·Introduction | 第46-47页 |
| ·Additive mappings preserving rank one nilpotent (resp.idempotent) operators | 第47-55页 |
| ·Applications | 第55-61页 |
| 7 Jordan Triple Maps on Standard Operator Algebras:The Two-dimensional Case | 第61-69页 |
| 8 Ideals, Filters and States on D-posets | 第69-84页 |
| ·Introduction | 第69-70页 |
| ·D-posets | 第70-74页 |
| ·Ideals and filters in D-posets | 第74-76页 |
| ·Supports, local ideals and local filters in D-posets | 第76-78页 |
| ·Sets of states on D-posets | 第78-84页 |
| 9 Ideals,Filters and Supports in Pseudoeffect Algebras | 第84-94页 |
| ·Introduction and preliminaries | 第84-86页 |
| ·Ideals and filters in pseudoeffect algebras | 第86-90页 |
| ·Supports, local filters and local ideals in pseudoeffect algebras | 第90-94页 |
| Bibliography | 第94-100页 |
| Appendix | 第100页 |
