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Minimal and Maximal Operator Theory With Applications

Published online by Cambridge University Press:  20 November 2018

M. W. Wong
M. W. Wong*
Affiliation:
Department of Mathematics and Statistics York University4700 Keele Street North York, Ontario M3J1P3
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Abstract

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Let X be a complex Banach space and A a linear operator from X into X with dense domain. We construct the minimal and maximal operators of the operator A and prove that they are equal under reasonable hypotheses on the space X and operator A. As an application, we obtain the existence and regularity of weak solutions of linear equations on the space X. As another application we obtain a criterion for a symmetric operator on a complex Hilbert space to be essentially self-adjoint. An application to pseudo-differential operators of the Weyl type is given.

Keywords

17B5017B20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 3 , 01 June 1991 , pp. 617 - 627
Copyright
Copyright © Canadian Mathematical Society 1991

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