Rigidity of weighted composition operators on H^p

2018/09/13 by Lindström, Mikael, Miihkinen, Santeri, Nieminen, Pekka J.
#47B10 #47B33 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1809.05118

Abstract

We show that every non-compact weighted composition operator f ↦ u⋅ (f∘ϕ) acting on a Hardy space H^p for 1 ≤ p < ∞ fixes an isomorphic copy of the sequence space ℓ^p and therefore fails to be strictly singular. We also characterize those weighted composition operators on H^p which fix a copy of the Hilbert space ℓ². These results extend earlier ones obtained for unweighted composition operators.

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