Maps preserving maximal numerical range of operator products

AbstractLet be a complex Hilbert space and denote by the algebra of all linear bounded operators on . For any , denote by V0(T) its maximal numerical range. We prove that if is a surjective map such thatfor any then there exists a unitary operator such that ϕ(T ) = ±UTU* (resp. ϕ(T) = λUTU* with |λ| = 1) for any .Mathematics Subject Classification (2020): Primary: 15A8647A1247B49Key words: Linear preserversmaximal numerical range