Arazy-Cwikel property for quasi-Banach couples
arXiv:2111.11782 · doi:10.1007/s11117-022-00936-8
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.
27 pages