## Banach Journal of Mathematical Analysis

### The carrier graph topology

#### Abstract

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

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

Dates
First available in Project Euclid: 14 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1313362980

Digital Object Identifier
doi:10.15352/bjma/1313362980

Mathematical Reviews number (MathSciNet)
MR2738520

Zentralblatt MATH identifier
1226.47012

#### Citation

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