The Horn-Li-Merino formula for the gap and the spherical gap of unbounded operators
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Abstract:
In this article we obtain the Horn-Li-Merino formula for computing the gap as well as the spherical gap between two densely defined unbounded closed operators. As a consequence we prove that the gap and the spherical gap of an unbounded closed operator are $1$ and $\sqrt {2}$ respectively. With the help of these formulae we establish a relation between the spherical gap and the gap of unbounded closed operators. We discuss some properties of the spherical gap similar to those of the gap metric.References
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Additional Information
- G. Ramesh
- Affiliation: Statistics and Mathematics Unit, Indian Statistical Institute Bangalore, Bangalore, India 560 059
- Email: ramesh@isibang.ac.in
- Received by editor(s): October 14, 2009
- Received by editor(s) in revised form: April 2, 2010
- Published electronically: October 1, 2010
- Additional Notes: The author is thankful to the NBHM for financial support and ISI Bangalore for providing necessary facilities to carry out this work.
- Communicated by: Marius Junge
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1081-1090
- MSC (2010): Primary 47A55
- DOI: https://doi.org/10.1090/S0002-9939-2010-10557-9
- MathSciNet review: 2745658