Arazy-Cwikel property for quasi-banach couples

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. Moreover, we show 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. This complements and refines previous results by Arazy-Cwikel and Bykov-Ovchinnikov even in the case of Banach spaces. We apply results obtained to some classical families of spaces. © 2022 Elsevier B.V., All rights reserved.