Abstract
Let be a complex Hilbert space and denote by the algebra of all linear bounded operators on . For any , denote by V 0(T) its maximal numerical range. We prove that if is a surjective map such that for any then there exists a unitary operator such that ϕ(T ) = ±UTU* (resp. ϕ(T) = λUTU* with |λ| = 1) for any .
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