Interpolation properties of $K$-monotone couples of quasi-Banach spaces

We plan to discuss recent results (see [1, 2, 3]) related to interpolation properties of couples of quasi-Banach spaces. In particular, new sufficient conditions, under which such a couple has the so-called Arazy-Cwikel prop- erty, will be considered. We give also some applications.

References

1. S. V. Astashkin, M. Cwikel, P. G. Nilsson, “Arazy-Cwikel and Calder ón-Mityagin type properties of the couples $(l^p, l^q ), 0 \le p \lt q \le \infty$”, Annali di Matematica Pura ed Applicata, 2022
2. S. V. Astashkin, P. G. Nilsson, “Arazy-Cwikel property for quasi-Banach couples”, Positivity, 26:4 (2022), 72  
3. S. V. Astashki, P. G. Nilsson, “A description of interpolation spaces for quasi-Banach couples by real $K$-method”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat, 117 (2023), 35