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 | References | Similar Articles | Additional Information

Abstract: In this paper we will investigate the selfadjointness of unbounded -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 -representation is standard.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0712267-5

Keywords:
-algebra,
(closed, selfadjoint, standard) representation

Article copyright:
© Copyright 1983
American Mathematical Society