The paper on computable presentations of separable Lebesgue spaces establishes conditions under which Lp spaces themselves can be given computable structure, but a deeper question remains untouched: can we algorithmically recognize when a bounded linear operator between two such computably presented Lp spaces is itself computable in the sense of computable analysis? The question asks whether there is a general decision procedure that takes as input an effective description of an operator and outputs a verdict on its computability, or whether this recognition problem is undecidable or even non-arithmetical in the descriptive set theoretic hierarchy. This sits at the intersection of computable functional analysis, the theory of representations of continuous structures, and the complexity of index sets in computability theory.