On the Lipschitz operator ideal Lip₀∘ \mathcal A∘ Lip₀

2022/11/25 by Albarracín, Nahuel, Turco, Pablo
#46B08 #47B10 #47H99 #47L20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2211.14240

Abstract

We study a systematic way to produce a Lipschitz operator ideal from a Banach linear operator ideal \mathcal A. For maximal and minimal operator ideals \mathcal A, the Lipschitz maximal hull and minimal kernel of the Lipschitz operator ideals Lip₀ ∘ \mathcal A ∘ Lip₀ are investigated, respectively. Using ultraproduct techniques, we obtain the Lipschitz version of a result of Kürsten and Piestch which characterizes the maximal hull of any Lipschitz operator ideal. Among other results, we characterize the linear operators which belong to Lip₀∘ \mathcal A∘ Lip₀ which, in many cases, they are precisely those which are in \mathcal A. In particular, we give some cases in which a nonlinear factorization of linear operators implies a linear one, in terms of a given Banach linear operator ideal \mathcal A.

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