Characterization of Lie centralizable mappings on B(X)
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929695755337728 |
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| author | Fadaee, Behrooz Ghahramani, Hoger Majidi, Ayyoub |
| author_facet | Fadaee, Behrooz Ghahramani, Hoger Majidi, Ayyoub |
| contents | Assume that B(X) is the algebra of all bounded linear operators on a complex Banach space X, and let W in B(X) is such that cl(W(X)) is not equal to X or W=zI, where z is a complex number and I is the identity operator. We show that if f: B(X) --> B(X) is an additive mapping Lie centralizable at W, then f(A)=kA+h(A) for all A in B(X), where k is a complex number and h:B(X)--> CI is an additive mapping such that h([A,B])=0 for all A,B in B(X) with AB=W. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of Lie centralizable mappings on B(X) Fadaee, Behrooz Ghahramani, Hoger Majidi, Ayyoub Functional Analysis Operator Algebras Assume that B(X) is the algebra of all bounded linear operators on a complex Banach space X, and let W in B(X) is such that cl(W(X)) is not equal to X or W=zI, where z is a complex number and I is the identity operator. We show that if f: B(X) --> B(X) is an additive mapping Lie centralizable at W, then f(A)=kA+h(A) for all A in B(X), where k is a complex number and h:B(X)--> CI is an additive mapping such that h([A,B])=0 for all A,B in B(X) with AB=W. |
| title | Characterization of Lie centralizable mappings on B(X) |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2502.01213 |