BEST POSSIBLE COMPACTNESS RESULTS OF LIONS–PEETRE TYPE

Fernando Cobos, Michael Cwikel, Pedro Matos
2001 Proceedings of the Edinburgh Mathematical Society  
If T : A 0 → B boundedly and T : A 1 → B compactly, then a result of Lions-Peetre shows that T : A → B compactly for a certain class of spaces A which are intermediate with respect to A 0 and A 1 . We investigate to what extent such results can hold for arbitrary intermediate spaces A. The 'dual' case of an operator S such that S : X → Y 0 boundedly and S : X → Y 1 compactly, is also considered, as well as similar questions for other closed operator ideals.
doi:10.1017/s0013091598001163 fatcat:74gkent3m5fxrdiv64ggbc3pni