Geodesic
On the essential self-adjointness of various algebras of field operators
Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 311-314 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that any $On^*$-algebra generated by a Wick polynomial in the free field and the particle number operator is essentiaily self-adjoint. 
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W. Timmerman; G. Lassner. On the essential self-adjointness of various algebras of field operators. Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 311-314. http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a2/

[1] A. N. Vasilev, N. V. Borisov, TMF, 11 (1972), 1 | MR

[2] G. Lassner, Topological algebras of operators, Preprint, Dubna, 1969 | MR

[3] A. Uhlmann, Über die Algebra der Feldoperatoren, Preprint, Leipzig, 1963

[4] A. N. Vasilev, TMF, 3 (1970), 1 | MR

[5] J. Glimm, A. Jaffe, Phys. Rev., 176 (1968), 000 | DOI | MR

[6] T. Kato, Perturbation theory for linear operators, Springer-Verlag, New York, 1966 | MR