Abstract
A famous result of S. Kwapień asserts that a linear operator from a Banach space to a Hilbert space is absolutely 1-summing whenever its adjoint is absolutely q-summing for some 1 ≤ q < ∞; this result was recently extended to Lipschitz operators by Chen and Zheng. In the present paper we show that Kwapień’s and Chen-Zheng’s theorems hold in a very relaxed nonlinear environment, under weaker hypotheses. Even when restricted to the original linear case, our result generalizes Kwapień’s theorem because it holds when the adjoint is just almost summing. In addition, a variant for \({{\cal L}_p}\)-spaces, with p ≥ 2, instead of Hilbert spaces, is provided.
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The authors are deeply indebted to the anonymous reviewer for his/her careful reading and insightful remarks and comments that helped to improve the final version of this paper.
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Renato Macedo is partially supported by Capes.
Daniel Pellegrino is supported by CNPq and Grant 2019/0014 Paraíba State Research Foundation (FAPESQ).
Joedson Santos is supported by CNPq and Grant 2019/0014 Paraíba State Research Foundation (FAPESQ).
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Macedo, R., Pellegrino, D. & Santos, J. Nonlinear variants of a theorem of Kwapień. Isr. J. Math. 247, 217–231 (2022). https://doi.org/10.1007/s11856-021-2258-2
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DOI: https://doi.org/10.1007/s11856-021-2258-2