Abstract
Let H and K be two complex separable Hilbert spaces, such that dim ( H ) ≥ 2 and B ( H ) the algebra of bounded linear operators of H on itself. For every A , B ∈ B ( H ) , the semistar Jordan product is denoted by A ▹ B = 1 2 ( AB + B ∗ A ) and for every λ ∈ [ 0 , 1 ] , the λ-Aluthge transform of A is denoted by Δ λ ( A ) . We show that a bijective map Φ : B ( H ) ⟶ B ( K ) satisfies the following condition for some λ ∈ ( 0 , 1 ) , Δ λ ( Φ ( A ) ▹ Φ ( B ) ) = Φ ( Δ λ ( A ▹ B ) ) , forall A , B ∈ B ( H ) , if and only if there exists a unitary or anti-unitary operator U : H ⟶ K , such that Φ ( A ) = UA U ∗ , forall A ∈ B ( H ) .
Published Version
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