Composition operators on Banach function spaces

Kumar, Rajeev; Kumar, Romesh

doi:10.1090/S0002-9939-05-07798-1

Composition operators on Banach function spaces
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Proc. Amer. Math. Soc. 133 (2005), 2109-2118 Request permission

Abstract:

We study the boundedness and the compactness of composition operators on some Banach function spaces such as absolutely continuous Banach function spaces on a $\sigma$–finite measure space, Lorentz function spaces on a $\sigma$–finite measure space and rearrangement invariant spaces on a resonant measure space. In addition, we study some properties of the spectra of a composition operator on the general Banach function spaces.

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