On injective Jordan semi-triple maps of matrix algebras☆

@inproceedings{Lenjak2006OnIJ,
  title={On injective Jordan semi-triple maps of matrix algebras☆},
  author={Gorazd Le{\vs}njak and N N Sze},
  year={2006}
}
Abstract We show that every injective Jordan semi-triple map on the algebra M n ( F ) of all n × n matrices with entries in a field F (i.e. a map Φ : M n ( F ) → M n ( F ) satisfying Φ ( ABA ) = Φ ( A ) Φ ( B ) Φ ( A ) for every A and B in M n ( F ) ) is given by a map of the following form: there exist σ ∈ F , σ = ±1, an injective homomorphism ϕ of F and an invertible T ∈ M n ( F ) such that either Φ ( A ) = σ T - 1 A ϕ T for all A ∈ M n ( F ) , or Φ ( A ) = σ T - 1 A ϕ t T for all A ∈ M n ( F… CONTINUE READING