On the nonnegative rank of positive operatorsDrnovšek, Roman (Avtor) Kandić, Marko (Avtor) nonnegative rankordered vector spacespositive operatorsYudin coneIn this paper, we introduce the concept of a nonnegative rank of a positive operator $T: X \to Y$ between ordered vector spaces. In the case of nonnegative matrices, our definition agrees with the standard definition of a nonnegative rank. Under some natural and mild assumptions on the cone $Y_+$, we prove that the nonnegative rank and the rank agree whenever the rank is at most two. This can be considered as the infinite-dimensional version of [6, Theorem 4.1]. We also provide an example of a positive rank-three operator on the Banach lattice $C[0, 1]$ with an infinite nonnegative rank.20262026-11-10 08:37:27Članek v reviji190995UDK: 517.9ISSN pri članku: 0025-584XDOI: 10.1002/mana.70262COBISS_ID: 304519683sl