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 → T† is an isometry in this metric. We also investigate the relationships between the topology induced by this metric and the gap metric. © 2010 Mathematics Subject Classification.

Ramesh G

Department of Mathematics

S.H. Kulkarni

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Journal	Banach Journal of Mathematical Analysis
Publisher	Tusi Mathematical Research Group (TMRG)
ISSN	17358787