This correspondence presents corrections and further comments to our previous paper titled 'Equivalence relations between learnability, output-dissipativity and strict positive realness' (Arimoto and Naniwa 2000). It corrects (1) the previous definition of input-output 'invertibility' by assuming an additional continuity property of the system inverse operator, redefines exactly (2) the 'output-dissipativity' by adding a condition of invertibility, and presents (3) a further comment on the proof of Lemma 1. A diagram is given in order to clearly show interrelationships between these concepts.