A note on weighted composition operators on measurable function spaces. (English) Zbl 1060.47032

The author considers the weighted composition operators \(W=uC_{\tau}\) between \(L^p(X,\Sigma,\mu)\) spaces and Orlicz spaces \(L^{\varphi}(X,\Sigma,\mu)\), generated by measurable and non-singular transformations \(\tau\) from \(X\) into itself and measurable functions \(u\) on \(X\). He characterizes the functions \(u\) and transformations \(\tau\) that induce weighted composition operators between \(L^p\)-space by using some properties of the conditional expectation operator, the pair \((u,\tau)\) and the measure space \((X,\Sigma,\mu)\). Some other properties of these operators are also investigated in this paper.


47B33 Linear composition operators
47B20 Subnormal operators, hyponormal operators, etc.
47B38 Linear operators on function spaces (general)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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