Abstract
We study the Banach–Stone theorem in the framework of Hilbert $$C^*$$ -modules and Finsler $$C^*$$ -modules and show that each $$\varphi $$ -morphism T between Hilbert $$C^*$$ -modules and Finsler $$C^*$$ -modules is a weighted composition operator of the form $$Tf(y) = h(y)f(\theta (y))$$ .
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