Composition operators with surjective symbol and small approximation numbers

Abstract : We give a new proof of the existence of a surjective symbol whose associated composition operator on H 2 (D) is in all Schatten classes, with the improvement that its approximation numbers can be, in some sense, arbitrarily small. We show, as an application, that, contrary to the 1-dimensional case, for N ≥ 2, the behavior of the approximation numbers a n = a n (C ϕ), or rather of β − N = lim inf n→∞ [a n ] 1/n 1/N or β + N = lim sup n→∞ [a n ] 1/n 1/N , of composition operators on H 2 (D N) cannot be determined by the image of the symbol. MSC 2010 Primary: 47B33 Secondary: 32A35 ; 46B28
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  • HAL Id : hal-01919077, version 1
  • ARXIV : 1811.05174

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Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza. Composition operators with surjective symbol and small approximation numbers. 2018. ⟨hal-01919077⟩

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