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Ascent and descent of weighted composition operators on \(L^p\)-spaces. (English) Zbl 1217.47048

Summary: We study weighted composition operators on \(L^p\)-spaces with finite ascent and descent. We also characterize the injective weighted composition operators.

MSC:

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