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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Positive symmetric quotients and their selfadjoint extensions


Authors: Saichi Izumino and Go Hirasawa
Journal: Proc. Amer. Math. Soc. 129 (2001), 2987-2995
MSC (2000): Primary 47A05, 47B25; Secondary 47A99
Published electronically: March 29, 2001
MathSciNet review: 1840104
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Abstract:

We define a quotient $B/A$ of bounded operators $A$ and $B$ on a Hilbert space $H$ with a kernel condition $\ker A\subset \ker B$ as the mapping $Au\to Bu$, $u\in H$. A quotient $B/A$ is said to be positive symmetric if $A^*B=B^*A\ge 0$. In this paper, we give a simple construction of positive selfadjoint extensions of a given positive symmetric quotient $B/A$.


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Additional Information

Saichi Izumino
Affiliation: Department of Mathematics, Faculty of Education, Toyama University, Toyama 930-0855, Japan
Email: izumino@edu.toyama-u.ac.jp

Go Hirasawa
Affiliation: Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05958-5
PII: S 0002-9939(01)05958-5
Keywords: Selfadjoint extension, symmetric operator, quotient of operators, symmetric quotient
Received by editor(s): March 12, 1998
Received by editor(s) in revised form: April 5, 1999, and February 28, 2000
Published electronically: March 29, 2001
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society