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Spatial theory for algebras of unbounded operators. II


Authors: A. Inoue and K. Takesue
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
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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 [Enhancements On Off] (What's this?)

  • [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertian, 2é ed., Gauthier-Villars, Paris, 1969.
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  • [3] A. Inoue, Operator-representations and vector-representations of positive linear functionals, Fukuoka Univ. Rep. (to appear).
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  • [7] A. Uhlmann, Properties of the algebra $ {L^ + }(D)$, JINR, Comm. E2-8149, Dubna, 1974.

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DOI: https://doi.org/10.1090/S0002-9939-1983-0681837-0
Article copyright: © Copyright 1983 American Mathematical Society

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