Crossed products of -dynamical systems with ground states

Author:
Masaharu Kusuda

Journal:
Proc. Amer. Math. Soc. **89** (1983), 273-278

MSC:
Primary 46L55; Secondary 46L40

DOI:
https://doi.org/10.1090/S0002-9939-1983-0712636-9

MathSciNet review:
712636

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Abstract: Let be the crossed product associated with a -dynamical system . We show that if there is a ground state for . then there is an ideal in such that if , then . where is the dual automorphism group on , and such that . Conversely, we show that if is unital, and if has such a decomposition for some proper ideal . then has a ground state.

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0712636-9

Article copyright:
© Copyright 1983
American Mathematical Society