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On the Adjoint and the Closure of the Sum of Two Unbounded Operators

Published online by Cambridge University Press:  20 November 2018

Mohammed Hichem Mortad
Mohammed Hichem Mortad*
Affiliation:
Department of Mathematics, University of Oran Es-Senia, BP 1524 El Menouar, 31000 Oran, Algeria, Mailing Address: BP 7085 Seddikia, Oran 31013, Algeria e-mail: mhmortad@gmail.commortad@univ-oran.dz
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Abstract

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We prove, under some conditions on the domains, that the adjoint of the sum of two unbounded operators is the sum of their adjoints in both Hilbert and Banach space settings. A similar result about the closure of operators is also proved. Some interesting consequences and examples “spice up” the paper.

Keywords

47A05unbounded operatorssum and products of operatorsHilbert and Banach adjointsself-adjoint operatorsclosed operatorsclosure of operators
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 3 , 01 September 2011 , pp. 498 - 505
Copyright
Copyright © Canadian Mathematical Society 2011

References

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