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

DOI:
https://doi.org/10.1090/S0002-9939-01-05958-5

Published electronically:
March 29, 2001

MathSciNet review:
1840104

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We define a quotient of bounded operators and on a Hilbert space with a kernel condition as the mapping , . A quotient is said to be positive symmetric if . In this paper, we give a simple construction of positive selfadjoint extensions of a given positive symmetric quotient .

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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:
https://doi.org/10.1090/S0002-9939-01-05958-5

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