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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Spatial theory for algebras of unbounded operators. II
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by A. Inoue and K. Takesue PDF
Proc. Amer. Math. Soc. 87 (1983), 295-300 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.
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Additional 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