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Bernd Thaller

Institut f. Mathematik
Universität Graz
A-8010 Graz, Austria
e-mail: bernd.thaller@kfunigraz.ac.at

A criterion for essential self-adjointness


We prove some facts about the essential self-adjointness of a symmetric operator T in a Hilbert space H. The main tools are bounded commutators of T with a suitable sequence of bounded self-adjoint operators. A special case is a Theorem of Jörgens and Chernoff stating that the essential self-adjointness of the Dirac operator in an external field depends only on the local properties of the potential.

(Journal of Operator Theory, 31 (1994), 351-361)

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Bernd Thaller
Institute of Mathematics
University of Graz.

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