J4 ›› 2011, Vol. 46 ›› Issue (8): 1-3.

• Articles •     Next Articles

Jordan multiplicative isomorphisms on Spin factors

JI Pei-sheng, SUN Lin, CHEN Jian-hui   

  1. School of Mathematics, Qingdao University, Qingdao 266071, Shandong, China
  • Received:2010-06-24 Online:2011-08-20 Published:2011-09-08


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

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