Banach Journal of Mathematical Analysis

The carrier graph topology

S. H. Kulkarni and G. Ramesh

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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.

Article information

Banach J. Math. Anal., Volume 5, Number 1 (2011), 56-69.

First available in Project Euclid: 14 August 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A50: Equations and inequalities involving linear operators, with vector unknowns
Secondary: 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]

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


Kulkarni, S. H.; Ramesh, G. The carrier graph topology. Banach J. Math. Anal. 5 (2011), no. 1, 56--69. doi:10.15352/bjma/1313362980.

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