On a problem of Lions concerning real interpolation spaces. The quasi-Banach case

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Cobos, Fernando and Cwikel, M. and Kühn, Thomas (2022) On a problem of Lions concerning real interpolation spaces. The quasi-Banach case. Journal of Mathematical Analysis and Applications . p. 126634. ISSN 0022-247X

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Official URL: https://doi.org/10.1016/j.jmaa.2022.126634



Abstract

We prove that, under a mild condition on a couple (A0;A1) of quasi-Banach spaces, all real interpolation spaces (A0;A1)θ,p with 0 < θ < 1 and 0 < p ≤ ∞ are different from each other. In the Banach case and for 1 ≤ p ≤ ∞ this was shown by Janson, Nilsson, Peetre and Zafran, thus solving an old problem posed by J.-L. Lions. Moreover, we give an application to certain spaces which are important objects in Operator Theory and which consist of bounded linear operators whose approximation numbers belong to Lorentz sequence spaces.


Item Type:Article
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CRUE-CSIC (Acuerdos Transformativos 2022)

Uncontrolled Keywords:Real interpolation; K-functional; Dependence on the parameters; Spaces of operators defined by approximation numbers.
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:74277
Deposited On:01 Sep 2022 15:19
Last Modified:15 Sep 2022 07:20

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