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Preserving operators on semiprime \(f\)-algebras. (English) Zbl 07490123

Summary: It is an open problem whether a separating operator acting between semiprime \(f\)-algebras is a weighted composition operator. In this respect, we have been largely motivated by the recent paper (Abid et al. in Positivity 21:521–537, 2017) which give a positive answer when the \(f\)-algebra domain is unital. In the general case, we prove that the answer is positive if and only if the separating operator is almost contractive. As a consequence, we generalizes and improve some well-known results on separating operators.

MSC:

06F25 Ordered rings, algebras, modules
46E25 Rings and algebras of continuous, differentiable or analytic functions
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References:

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