Derivations with values in noncommutative symmetric spaces
Let $E=E(0,\infty )$ be a symmetric function space and $E(\mathcal{M},\tau )$ be the noncommutative symmetric space corresponding to $E(0,\infty )$ associated with a von Neumann algebra with a faithful normal semifinite trace. Our main result identifies the class of spaces $E$ for which every deriva...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-10-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.508/ |
| _version_ | 1797638562698493952 |
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| author | Huang, Jinghao Sukochev, Fedor |
| author_facet | Huang, Jinghao Sukochev, Fedor |
| author_sort | Huang, Jinghao |
| collection | DOAJ |
| description | Let $E=E(0,\infty )$ be a symmetric function space and $E(\mathcal{M},\tau )$ be the noncommutative symmetric space corresponding to $E(0,\infty )$ associated with a von Neumann algebra with a faithful normal semifinite trace. Our main result identifies the class of spaces $E$ for which every derivation $\delta :\mathcal{A}\rightarrow E(\mathcal{M},\tau )$ is necessarily inner for each $C^*$-subalgebra $\mathcal{A}$ in the class of all semifinite von Neumann algebras $\mathcal{M}$ as those with the Levi property. |
| first_indexed | 2024-03-11T13:05:22Z |
| format | Article |
| id | doaj.art-3a5319cd334f44aebd2e3002e995a36e |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T13:05:22Z |
| publishDate | 2023-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-3a5319cd334f44aebd2e3002e995a36e2023-11-03T14:36:25ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-10-01361G81357136510.5802/crmath.50810.5802/crmath.508Derivations with values in noncommutative symmetric spacesHuang, Jinghao0Sukochev, Fedor1Institute for Advanced Study in Mathematics of HIT, Harbin Institute of Technology, Harbin, 150001, ChinaSchool of Mathematics and Statistics, University of New South Wales, Kensington, 2052, AustraliaLet $E=E(0,\infty )$ be a symmetric function space and $E(\mathcal{M},\tau )$ be the noncommutative symmetric space corresponding to $E(0,\infty )$ associated with a von Neumann algebra with a faithful normal semifinite trace. Our main result identifies the class of spaces $E$ for which every derivation $\delta :\mathcal{A}\rightarrow E(\mathcal{M},\tau )$ is necessarily inner for each $C^*$-subalgebra $\mathcal{A}$ in the class of all semifinite von Neumann algebras $\mathcal{M}$ as those with the Levi property.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.508/derivationnoncommutative symmetric spacesemifinite von Neumann algebra |
| spellingShingle | Huang, Jinghao Sukochev, Fedor Derivations with values in noncommutative symmetric spaces Comptes Rendus. Mathématique derivation noncommutative symmetric space semifinite von Neumann algebra |
| title | Derivations with values in noncommutative symmetric spaces |
| title_full | Derivations with values in noncommutative symmetric spaces |
| title_fullStr | Derivations with values in noncommutative symmetric spaces |
| title_full_unstemmed | Derivations with values in noncommutative symmetric spaces |
| title_short | Derivations with values in noncommutative symmetric spaces |
| title_sort | derivations with values in noncommutative symmetric spaces |
| topic | derivation noncommutative symmetric space semifinite von Neumann algebra |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.508/ |
| work_keys_str_mv | AT huangjinghao derivationswithvaluesinnoncommutativesymmetricspaces AT sukochevfedor derivationswithvaluesinnoncommutativesymmetricspaces |