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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Standard systems for semifinite O$^{*}$-algebras
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by Atsushi Inoue PDF
Proc. Amer. Math. Soc. 125 (1997), 3303-3312 Request permission

Abstract:

We shall continue the study of standard systems which make it possible to develop the Tomita-Takesaki theory in O$^*$-algebras. The main purpose of this paper is to give the necessary and sufficient conditions for which a standard system $(\mathcal {M}, \lambda , \lambda ’)$ of an O$^*$-algebra $\mathcal {M}$, a generalized vector $\lambda$ and the commutant $\lambda ’$ is unitarily equivalent to a standard system $\bigl ( \mathcal {N}, K’ \mu , (K’ \mu )’\bigr )$ constructed by a standard tracial generalized vector $\mu$ for an O$^*$-algebra $\mathcal {N}$ and a non-singular positive self-adjoint operator $K’$ affiliated with the commutant $\mathcal {N}’_{ \mathrm {w}}$ of $\mathcal {N}$.
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Additional Information
  • Atsushi Inoue
  • Affiliation: Department of Applied Mathematics, Fukuoka University, Fukuoka, 814-80, Japan
  • Email: sm010888ssat.fukuoka-u.ac.jp
  • Received by editor(s): June 12, 1996
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3303-3312
  • MSC (1991): Primary 47D40; Secondary 46K15, 46L10
  • DOI: https://doi.org/10.1090/S0002-9939-97-03962-2
  • MathSciNet review: 1403134