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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.

MSC:
 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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