Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The Horn-Li-Merino formula for the gap and the spherical gap of unbounded operators

Author: G. Ramesh
Journal: Proc. Amer. Math. Soc. 139 (2011), 1081-1090
MSC (2010): Primary 47A55
Published electronically: October 1, 2010
MathSciNet review: 2745658
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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.

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Additional Information

G. Ramesh
Affiliation: Statistics and Mathematics Unit, Indian Statistical Institute Bangalore, Bangalore, India 560 059

Keywords: Closed operator, gap metric, spherical gap, Horn-Li-Merino formula
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.