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Selfadjoint representations of polynomial algebras


Authors: Atsushi Inoue and Kunimichi Takesue
Journal: Trans. Amer. Math. Soc. 280 (1983), 393-400
MSC: Primary 46K10; Secondary 46L99, 47D25
DOI: https://doi.org/10.1090/S0002-9947-1983-0712267-5
MathSciNet review: 712267
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Abstract: In this paper we will investigate the selfadjointness of unbounded $ ^{\ast}$-representations of the polynomial algebra. In particular, it is shown that the notion of selfadjoint representation is equivalent to that of standard representation in the case of the polynomial algebra generated by one hermitian element. Although the notion of standardness implies that of selfadjointness, the converse is not true in general. Therefore, we consider under what conditions a $ ^{\ast}$-representation is standard.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0712267-5
Keywords: $ O_p^{\ast}$-algebra, (closed, selfadjoint, standard) representation
Article copyright: © Copyright 1983 American Mathematical Society

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