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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

References

1. Folland, G.B., Harmonic analysis in phase space. Princeton University Press, 1989.Google Scholar
2. Hörmander, L., On the theory of general partial differential operators, Acta Math. 94(1955), 161–248.Google Scholar
3. Kumano-go, H., Pseudo-differential operators. MIT Press, 1981.Google Scholar
4. Reed, M. and Simon, B., Functional analysis. Revised and enlarged edition, Academic Press, 1980.Google Scholar
5. Schechter, M., Principles of functional analysis. Academic Press, 1971.Google Scholar
6. Schechter, M., Modern methods in partial differential equations. McGraw-Hill, 1977.Google Scholar
7. Schechter, M., Operator methods in quantum mechanics. North Holland, 1981.Google Scholar
8. Schechter, M., Spectra of partial differential operators. Second edition, North Holland, 1986.Google Scholar
9. Wong, M.W., LP-spectra of strongly Carleman pseudo-differential operators, J. Funct. Anal. 44(1981), 163–173.Google Scholar
10. Wong, M.W., On some spectral properties of elliptic pseudo-differential operators, Proc. Amer. Math. Soc. 99(1987), 683–689.Google Scholar
11. Wong, M.W., An introduction to pseudo-differential operators. World Scientific, 1991.Google Scholar