On Disjointly singular centralizers

We study “disjoint” versions of the notions trivial, locally strictly singular and super-strictly quasi-linear maps in context Köthe function spaces. Among other results, we show: (i) (locally) trivial disjointly coincide on reflexive spaces; (ii) non-atomic superreflexive spaces, no centralizer is singular, although most are singular. (iii) supersingular exist between spaces Kalton—Peck centralizers super-disjointly singular; (iv) disjoint singularity does not imply super-disjoint singularity.