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Journal of Mathematics
Volume 2014, Article ID 265349, 4 pages
Research Article

Essential Self-Adjointness of Anticommutative Operators

Faculty of Science and Technology, Gunma University, Gunma 376-8515, Japan

Received 30 January 2014; Accepted 6 March 2014; Published 27 March 2014

Academic Editor: Jen-Chih Yao

Copyright © 2014 Toshimitsu Takaesu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The self-adjoint extensions of symmetric operators satisfying anticommutation relations are considered. It is proven that an anticommutative type of the Glimm-Jaffe-Nelson commutator theorem follows. Its application to an abstract Dirac operator is also considered.