Preserving operators on semiprime f-algebras

TL;DR

This paper investigates the nature of separating operators on semiprime f-algebras, establishing conditions under which they are weighted composition operators and extending existing results in the field.

Contribution

It proves that separating operators are weighted composition operators if and only if they are almost contractive, generalizing and strengthening previous results.

Findings

Separating operators are weighted composition operators under almost contractive condition

The result provides a solution to an open problem in the theory of f-algebras

Generalizes known results on separating operators in semiprime f-algebras

Abstract

It is an open problem whether a separating operator acting between semiprime f-algebras is a weighted composition operator ( <cite>AAB</cite>). We prove that the answer is positive if and only if the separating operator is almost contractive. As a consequence, we can generalized and strengthen some well-known results on separating operators.