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arXiv · 2111.11782

Arazy-Cwikel property for quasi-Banach couples

Sergey V. Astashkin·Per G. Nilsson
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Abstract

The main result of this paper establishes that the known Arazy-Cwikel property holds for classes of uniformly K-monotone spaces in the quasi-Banach setting provided that the initial couple is mutually closed. As a consequence, we get that the class of all quasi-Banach K-spaces (i.e., interpolation spaces which are described by the real K-method) with respect to an arbitrary mutually closed Banach couple enjoys the Arazy-Cwikel property. Another consequence complements some previous results by Bykov and Ovchinnikov, showing that this property holds also for the class of all interpolation quasi-Banach spaces with respect to a quasi-Banach couple whenever all the couples involved have the uniform Calderón-Mityagin property. We apply these results to some classical families of spaces.

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Sergey V. Astashkin, Per G. Nilsson. 2021-11-23. Arazy-Cwikel property for quasi-Banach couples. https://doi.org/10.1007/s11117-022-00936-8

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