Generalized Jordan Semitriple Maps on Hilbert Space Effect Algebras

Abstract EN

Let ℰ(H) be the Hilbert space effect algebra on a Hilbert space H with dimH≥3, α,β two positive numbers with 2α+β≠1 and Φ:ℰ(H)→ℰ(H) a bijective map.

We show that if Φ(AαBβAα)=Φ(A)αΦ(B)βΦ(A)α holds for all A,B∈ℰ(H), then there exists a unitary or an antiunitary operator U on H such that Φ(A)=UAU* for every A∈ℰ(H).