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Zbl 1226.47012
Kulkarni, S.H.; Ramesh, G.
The carrier graph topology. (English)
[J] Banach J. Math. Anal. 5, No. 1, 56-69, electronic only (2011). ISSN 1735-8787/e

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 $T\mapsto T^\dagger$ is an isometry in this metric. We also investigate the relationships between the topology induced by this metric and the gap metric.

MSC 2000:: *47A50 Equations and inequalities involving linear operators
47A05 General theory of linear operators

Keywords: gap metric; carrier graph topology; reduced minimum modulus; Moore-Penrose inverse

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