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Composition operators in Orlicz spaces. (English) Zbl 1073.47032
The authors consider composition operators \(C_{\tau}\) between Orlicz spaces \(L^{\phi}(X,\Sigma,\mu)\), generated by measurable and non-singular transformations \(\tau\) from \(\Omega\) into itself. They characterize the boundedness and compactness of composition operators between Orlicz spaces in terms of properties of the mapping \(\tau\), the function \(\phi\) and the measure space \((X,\Sigma,\mu)\). These results generalize earlier results known for \(L^p\)-spaces.

MSC:
47B33 Linear composition operators
47B07 Linear operators defined by compactness properties
46B70 Interpolation between normed linear spaces
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