We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C *-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E *(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E *) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes [Proc. London Math. Soc. 49(1984), 289–306].
@article{bwmeta1.element.doi-10_2478_s11533-008-0057-1,
author = {Maria Joi\c ta},
title = {Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {73-83},
zbl = {1182.46054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0057-1}
}
Maria Joiţa. Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras. Open Mathematics, Tome 7 (2009) pp. 73-83. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0057-1/
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