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 | References | Similar Articles | Additional Information

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 and 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

Email:
ramesh@isibang.ac.in

DOI:
http://dx.doi.org/10.1090/S0002-9939-2010-10557-9

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.