J4 ›› 2011, Vol. 46 ›› Issue (8): 1-3.
• 论文 • 下一篇
纪培胜,孙琳,陈剑慧
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国家自然科学基金资助项目(10971117)
JI Pei-sheng, SUN Lin, CHEN Jian-hui
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摘要:
设R是实数域,H是维数大于1的实的Hilbert空间, A=H十 R是相应于H的Spin因子。 如果A上的双射Ø满足任给x,y∈A都有Ø(x。y)=Ø(x)+Ø(y), 并且任给α,β∈R有Ø(α+β)=Ø(α)+Ø(β), 则H上存在酉算子U使得任给a∈H, α∈R都有Ø(a+α)=Ua+α。
关键词: Spin因子; Jordan可乘同构; 可加性
Abstract:
Let R be the field of real numbers and H be a real Hilbert space of dimension at least 2. Let A=H十R be the Spin factor corresponding to H. In this note, we prove that if a bijective map Ø from A onto itself satisfies Ø(x。y)=Ø(x)。Ø(y) for all x,y∈A, and Ø(α+β)=Ø(α)+Ø(β) for all α,β∈R, then there is a unitary operator U on H such that Ø(a+α)=Ua+α for every a∈H, α∈R.
Key words: Spin factor; Jordan multiplicative isomorphism; additivity
纪培胜,孙琳,陈剑慧. Spin因子上的Jordan可乘同构[J]. J4, 2011, 46(8): 1-3.
JI Pei-sheng, SUN Lin, CHEN Jian-hui. Jordan multiplicative isomorphisms on Spin factors[J]. J4, 2011, 46(8): 1-3.
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