Characterizing Derivations on Von Neumann Algebras by Local Actions
Let ℳ be any von Neumann algebra without central summands of type I1 and P a core-free projection with the central carrier I. For any scalar ξ, it is shown that every additive map L on ℳ satisfies L(AB-ξBA)=L(A)B-ξBL(A)+AL(B)-ξL(B)A whenever AB=P if and only if (1) ξ=1, L=φ+h, where φ is an additive...
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Hindawi Limited
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/407427 |
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doaj-f8efb606ca9f47d5b53d788aed28b7c22020-11-24T23:29:41ZengHindawi LimitedJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/407427407427Characterizing Derivations on Von Neumann Algebras by Local ActionsXiaofei Qi0Jia Ji1Department of Mathematics, Shanxi University, Taiyuan 030006, ChinaDepartment of Mathematics, Shanxi University, Taiyuan 030006, ChinaLet ℳ be any von Neumann algebra without central summands of type I1 and P a core-free projection with the central carrier I. For any scalar ξ, it is shown that every additive map L on ℳ satisfies L(AB-ξBA)=L(A)B-ξBL(A)+AL(B)-ξL(B)A whenever AB=P if and only if (1) ξ=1, L=φ+h, where φ is an additive derivation and h is a central valued additive map vanishing on AB-BA with AB=P; (2) ξ≠1, L is a derivation with L(ξA)=ξL(A) for each A∈ℳ.http://dx.doi.org/10.1155/2013/407427 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Xiaofei Qi Jia Ji |
| spellingShingle |
Xiaofei Qi Jia Ji Characterizing Derivations on Von Neumann Algebras by Local Actions Journal of Function Spaces and Applications |
| author_facet |
Xiaofei Qi Jia Ji |
| author_sort |
Xiaofei Qi |
| title |
Characterizing Derivations on Von Neumann Algebras by Local Actions |
| title_short |
Characterizing Derivations on Von Neumann Algebras by Local Actions |
| title_full |
Characterizing Derivations on Von Neumann Algebras by Local Actions |
| title_fullStr |
Characterizing Derivations on Von Neumann Algebras by Local Actions |
| title_full_unstemmed |
Characterizing Derivations on Von Neumann Algebras by Local Actions |
| title_sort |
characterizing derivations on von neumann algebras by local actions |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces and Applications |
| issn |
0972-6802 1758-4965 |
| publishDate |
2013-01-01 |
| description |
Let ℳ be any von Neumann algebra without central summands of type I1 and P a core-free projection with the central carrier I. For any scalar ξ, it is shown that every additive map L on ℳ satisfies L(AB-ξBA)=L(A)B-ξBL(A)+AL(B)-ξL(B)A whenever AB=P if and only if (1) ξ=1, L=φ+h, where φ is an additive derivation and h is a central valued additive map vanishing on AB-BA with AB=P; (2) ξ≠1, L is a derivation with L(ξA)=ξL(A) for each A∈ℳ. |
| url |
http://dx.doi.org/10.1155/2013/407427 |
| work_keys_str_mv |
AT xiaofeiqi characterizingderivationsonvonneumannalgebrasbylocalactions AT jiaji characterizingderivationsonvonneumannalgebrasbylocalactions |
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1725544424092467200 |