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| Higher Dimensional Numerical Range of Generalized (Jordan) Product ofOperators |
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Citation： |
Shaoxing SUN ·,Xiaofei QI ·,Ting ZHANG.Higher Dimensional Numerical Range of Generalized (Jordan) Product ofOperators[J].Chinese Annals of Mathematics B,2026,(5):771~802 |
| Page view： 5
Net amount： 7 |
Authors： |
Shaoxing SUN ·; Xiaofei QI ·;Ting ZHANG |
Foundation： |
the National Natural Science Foundation of China (Nos. 12571138,
12171290, 12301152), the Shanxi Scholarship Council of China (No. 2025-001) and the Natural Science
Basic Research Program of Shaanxi Province (No. S2025-JC-QN-1854). |
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| Abstract： |
Let H be a complex Hilbert space. Denote by B(H) and Bs(H) the algebra of all
bounded linear operators on H and the Jordan algebra of all self-adjoint operators in B(H),
respectively. In this paper, the authors first give some elementary properties about higher
dimensional numerical range of generalized (Jordan) product of operators in B(H). Based
on these results, all surjective maps on B(H) (respectively, Bs(H)) that preserve higher
dimensional numerical range of generalized (Jordan) product of operators are completely
characterized. Particularly, they give complete characterizations of all surjective maps
preserving higher dimensional numerical range of operator products, Jordan semi-triple
products and Jordan products on B(H) and Bs(H), respectively. |
Keywords： |
k-Dimensional numerical range Generalized product Generalized
Jordan product |
Classification： |
47B49 |
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