Topologies for O-Families with Metrizable Graph Topologies

Abstract

In the previous chapter some basic topologies on linear subspaces of 𝓛(𝓓 _𝓐 , 𝓓⁺ _𝓑) were introduced and general properties of these topologies were established. Assuming throughout that the graph topologies of the O-families resp. O*-algebras are metrizable, the present chapter continues the study of the topologies τ _𝓓 , τ _𝓝 , τ _O , τ ^𝓓 , τ ^𝓝 and τ ^O. There are a number of results which can be obtained under this additional assumption.