Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4624184 | Journal of Mathematical Analysis and Applications | 2006 | 12 Pages |
Abstract
Let Φ:A→B be an additive surjective map between some operator algebras such that AB+BA=0 implies Φ(A)Φ(B)+Φ(B)Φ(A)=0. We show that, under some mild conditions, Φ is a Jordan homomorphism multiplied by a central element. Such operator algebras include von Neumann algebras, C∗-algebras and standard operator algebras, etc. Particularly, if H and K are infinite-dimensional (real or complex) Hilbert spaces and A=B(H) and B=B(K), then there exists a nonzero scalar c and an invertible linear or conjugate-linear operator U:H→K such that either Φ(A)=cUAU−1 for all A∈B(H), or Φ(A)=cUA∗U−1 for all A∈B(H).
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