Abstract.
Let A be a unital C *-algebra. An element u of A is unitary and belongs to the centre of A if and only if \( |\varphi (u)| = 1 \) for every pure state \( \varphi \). Using this fact we show that a numerical radius preserving linear isomorphism on A is a C *-isomorphism multiplied by a fixed unitary element in the centre of A.
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Received: 3.12.1996
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Chan, JT. Numerical radius preserving operators on C*-algebras. Arch. Math. 70, 486–488 (1998). https://doi.org/10.1007/s000130050223
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DOI: https://doi.org/10.1007/s000130050223