Some stronger topologies for closed operators in Hilbert space
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Int. J. Contemp. Math. Sciences
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