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The carrier graph topology. (English) Zbl 1226.47012
Summary: We define a new metric on the set of all closed linear operators between Hilbert spaces and investigate its properties. In particular, we show that the set of all closed operators with a closed range is an open subset of the set of all closed operators and the map TT is an isometry in this metric. We also investigate the relationships between the topology induced by this metric and the gap metric.
MSC:
47A50Equations and inequalities involving linear operators, with vector unknowns
47A05General theory of linear operators