Some remarks on the gap metric

This paper presents the following results on the gap metric defined on the space of closed linear operators: 1) the topology introduced by the gap metric is a diagonal product topology; 2) if the gap of two closed operators is smaller than one, then the two directed gaps are the same; 3) a normalized right coprime factorization is constructed for given densely defined closed linear operators, and using this result an equivalent form of the gap metric is presented. Keywords: Closed linear operator, the gap metric, normalized right coprime factorization.