Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ADDITIVITY OF LIE MAPS ON OPERATOR ALGEBRAS

  • Qian, Jia (DEPARTMENT OF MATHEMATICS NANJING UNIVERSITY OF AERONAUTICS AND ASTRONAUTICS) ;
  • Li, Pengtong (DEPARTMENT OF MATHEMATICS NANJING UNIVERSITY OF AERONAUTICS AND ASTRONAUTICS)
  • Published : 2007.05.31
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Abstract

Let A standard operator algebra which does not contain the identity operator, acting on a Hilbert space of dimension greater than one. If ${\Phi}$ is a bijective Lie map from A onto an arbitrary algebra, that is $${\phi}$$(AB-BA)=$${\phi}(A){\phi}(B)-{\phi}(B){\phi}(A)$$ for all A, B${\in}$A, then ${\phi}$ is additive. Also, if A contains the identity operator, then there exists a bijective Lie map of A which is not additive.

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References

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