Selfadjointness of -representations generated by positive linear functionals

Author:
A. Inoue

Journal:
Proc. Amer. Math. Soc. **93** (1985), 643-647

MSC:
Primary 47D40; Secondary 46K10

MathSciNet review:
776195

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Abstract: The first purpose of this paper is to prove that is selfadjoint when is selfadjoint and is bounded, where is the sum of positive linear functionals on a -algebra and and are -representations generated by and , respectively. The second purpose is to prove that is standard, where is a positive linear functional on such that there exists a net of positive linear functionals on satisfying is bounded for all and for each .

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0776195-9

Article copyright:
© Copyright 1985
American Mathematical Society