Spatial theory for algebras of unbounded operators. II
HTML articles powered by AMS MathViewer
- by A. Inoue and K. Takesue
- Proc. Amer. Math. Soc. 87 (1983), 295-300
- DOI: https://doi.org/10.1090/S0002-9939-1983-0681837-0
- PDF | Request permission
Abstract:
In the previous paper [6], we have studied the spatial theory of $O_p^ *$-algebras with a strongly cyclic vector. In this paper, we will investigate the spatial theory between $O_p^ *$-algebras induced by a positive invariant sesquilinear form, which contains the former result.References
- J. Dixmier, Les algèbres d’opérateurs dans l’espace Hilbertian, 2é ed., Gauthier-Villars, Paris, 1969.
- S. Gudder and W. Scruggs, Unbounded representations of $\ast$-algebras, Pacific J. Math. 70 (1977), no. 2, 369–382. MR 482269 A. Inoue, Operator-representations and vector-representations of positive linear functionals, Fukuoka Univ. Rep. (to appear).
- G. Lassner, Topological algebras of operators, Rep. Mathematical Phys. 3 (1972), no. 4, 279–293. MR 322527, DOI 10.1016/0034-4877(72)90012-2
- Robert T. Powers, Self-adjoint algebras of unbounded operators, Comm. Math. Phys. 21 (1971), 85–124. MR 283580
- K. Takesue, Spatial theory for algebras of unbounded operators, Rep. Math. Phys. 21 (1985), no. 3, 347–355. MR 804216, DOI 10.1016/0034-4877(85)90037-0 A. Uhlmann, Properties of the algebra ${L^ + }(D)$, JINR, Comm. E2-8149, Dubna, 1974.
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 295-300
- MSC: Primary 47D40; Secondary 46K05, 46L99
- DOI: https://doi.org/10.1090/S0002-9939-1983-0681837-0
- MathSciNet review: 681837