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2009 | 7 | 1 | 73-83
Tytuł artykułu

Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras

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EN
Abstrakty
EN
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].
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
1
Strony
73-83
Opis fizyczny
Daty
wydano
2009-03-01
online
2009-01-10
Twórcy
autor
Bibliografia
  • [1] Apostol C., b *-algebras and their representation, J. London Math. Soc. (2), 1971, 3, 30–38 http://dx.doi.org/10.1112/jlms/s2-3.1.30[Crossref]
  • [2] Bakić D., Extensions of Hilbert C *-modules, Houston J. Math., 2004, 30, 537–558
  • [3] Combes F., Crossed products and Morita equivalence, Proc. London Math. Soc., 1984, 49, 289–306 http://dx.doi.org/10.1112/plms/s3-49.2.289[Crossref]
  • [4] Fragoulopoulou M., Topological algebras with involution, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, 2005
  • [5] Inoue A., Locally C *-algebras, Mem. Faculty Sci. Kyushu Univ. Ser. A, 1971, 25, 197–235 http://dx.doi.org/10.2206/kyushumfs.25.197[Crossref]
  • [6] Joiţa M., Tensor products of Hilbert modules over locally C *-algebras, Czech. Math. J., 2004, 54(129), 727–737 http://dx.doi.org/10.1007/s10587-004-6421-9[Crossref]
  • [7] Joiţa M., Morita equivalence for locally C *-algebras, Bull. London Math. Soc., 2004, 36, 802–810 http://dx.doi.org/10.1112/S0024609304003522[Crossref]
  • [8] Joiţa M., On the linking algebra of a Hilbert module and strong Morita equivalence of locally C *-algebras, Surv. Math. Appl., 2006, 1, 23–32
  • [9] Joiţa M., A note on Morita equivalence of group actions on pro-C *-algebras, Rocky Mountain J. Math., to appear
  • [10] Joiţa M., Crossed products of locally C *-algebras and strong Morita equivalence, Mediterr. J. Math., 2008, 5, 467–492 http://dx.doi.org/10.1007/s00009-008-0162-1[WoS][Crossref]
  • [11] Joiţa M., Hilbert modules over locally C *-algebras, University of Bucharest Press, 2006
  • [12] Joiţa M., Countably generated Hilbert modules and stable isomorphisms of locally C *-algebras, In: Douglas R.G., Esterle J., Gaspar D., Timotin D., Vasilescu F.-H. (Eds.), Theta Ser. Adv. Math. Theta, Bucharest, 2008, 9, 89–99
  • [13] Joiţa M., A note on full countably generated Hilbert modules, preprint [WoS]
  • [14] Lance C.E., Hilbert C *-modules. A toolkit for operator algebraists, London Mathematical Society Lecture Note Series 210, Cambridge University Press, Cambridge, 1995
  • [15] Lassner G., Über Realisierungen gewisser *-Algebren, Math. Nachr., 1972, 52, 161–166 (in German) http://dx.doi.org/10.1002/mana.19720520113[Crossref]
  • [16] Pedersen G.K., C *-algebras and their automorphism groups, London Mathematical Society Monographs 14, Academic Press, London-New York, 1979
  • [17] Phillips N.C., Inverse limits of C *-algebras, J. Operator Theory, 1988, 19, 159–195
  • [18] Phillips N.C., Representable K-theory for σ-C *-algebras, K-Theory, 1989, 3, 441–478 http://dx.doi.org/10.1007/BF00534137[Crossref]
  • [19] Raeburn I., Thompson S.J., Countably generated Hilbert modules, the Kasparov stabilisation theorem, and frames with Hilbert modules, Proc. Amer. Math. Soc., 2003, 131, 1557–1564 http://dx.doi.org/10.1090/S0002-9939-02-06787-4[Crossref]
  • [20] Schmüdgen K., Über LMC-Algebren, Math. Nachr., 1975, 68, 167–182 (in German) http://dx.doi.org/10.1002/mana.19750680113[Crossref]
  • [21] Zhuraev Yu.I., Sharipov F., Hilbert modules over locally C *-algebras, preprint available at arXiv:math.OA/0011053
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0057-1
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