On maps compressing the numerical range between $C^*$-algebras

Document Type: Original Article


FSG Tunisia


In this paper, we deal with the problem of characterizing linear maps compressing the numerical range. A
counterexample is given to show that such a map need not be a Jordan *-homomorphism in general even if the C*-algebras are commutative. Next, under an auxiliary condition we show that such a map is a Jordan *-homomorphism.