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| 摘要: |
| 令H是复数域C上的Hilbert空间, B(H)表示H上所有有界线性算子构成的代数, C, D∈B(H)是任意两个固定算子.本文研究了B(H)上可加导子的局部刻画问题.利用算子分解的方法,证明了可加映射φ:B(H)→B(H)满足条件对任意A, B∈B(H), AB=C蕴涵φ(A)B+Aφ(B)=D成立当且仅当存在B(H)上的可加导子δ与数λ∈C使得φ(C)+λC=D且φ(A)=δ(A)+λA对所有A∈B(H)成立.该结果推广改进了已有的一些相关成果. |
| 关键词: 可加导子 局部导子 有界线性算子 Hilbert空间 |
| DOI： |
| 分类号:O177.1 |
| 基金项目:国家自然科学基金资助(12171290,12301152); 山西省自然科学基金资助(202203021222018). |
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| A NEW CHARACTERIZATION OF ADDITIVE DERIVATIONS ON B（H） |
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ZHANG Ting,YU Zhi-qiang,XU Bing,QI Xiao-fei
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| Abstract: |
| Let H be any complex Hilbert space and B(H) the algebra of all bounded linear operators on H, and let C, D ∈ B(H) be any two fixed operators. In this paper, we study the question of local characterization of additive derivations on B(H). By using operator block methods, we show that an additive map δ : B(H) → B(H) satisfies that, for any A, B ∈ B(H),AB = C implies φ（A）B + Aφ（B） = D, if and only if there exists some additive derivation δ on B(H) and λ ∈ C such that φ（C） + λC = D and φ（A） = δ（A） + λA for all A ∈ B(H). Our result generalizes and improves some known related ones. |
| Key words: Additive derivations local derivations bounded linear operators Hilbert space |
