Some stronger topologies for closed operators in Hilbert space

Abstract

The purpose of this paper is to introduce some new metrics on the set C(H) of closed densely defined operators on a Hilbert space H and we characterize the closure of the subset of bounded elements of C(H) for these metrics. We define the notion of quotient-convergence in C(H) and we show that the toplogy induced by quotient-convergence is strictly stronger than the topology induced from the gap metric. Mathematics Subject Classification: 47A45, 47A65