Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Morita equivalence and Pedersen ideals


Author: Pere Ara
Journal: Proc. Amer. Math. Soc. 129 (2001), 1041-1049
MSC (2000): Primary 46L08, 16D90
DOI: https://doi.org/10.1090/S0002-9939-00-05688-4
Published electronically: October 4, 2000
MathSciNet review: 1814143
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that two $C^{*}$-algebras are strongly Morita equivalent if and only if their Pedersen ideals are Morita equivalent as rings with involution.


References [Enhancements On Off] (What's this?)

  • [1] G. Abrams, Morita equivalence for rings with local units, Comm. in Algebra 11(8) (1983), 801-837. MR 85b:16037
  • [2] F.W. Anderson and K.R. Fuller, Rings and Categories of Modules (2nd ed.), Springer-Verlag, New York, 1992. MR 94i:16001
  • [3] P.N. Anh and L. Marki, Morita equivalence for rings without identity, Tsukuba J. Math. 11 (1987), 1-16. MR 88h:16054
  • [4] P. Ara, Morita equivalence for rings with involution, Algebras and Representation Theory 2 (1999), 227-247. CMP 2000:02
  • [5] W. Beer, On Morita equivalence of nuclear $C^{*}$-algebras, J. Pure Applied Algebra 26 (1982), 249-267. MR 84d:46096
  • [6] D. Blecher, On Morita's Fundamental Theorem for $C^{*}$-algebras, to appear in Math. Scand.
  • [7] L.G. Brown, P. Green and M.A. Rieffel, Stable isomorphism and strong Morita equivalence of $C^{*}$-algebras, Pacific J. Math. 71 (1977), 349-363. MR 57:3866
  • [8] L.G. Brown, J.A. Mingo and N.T. Shen, Quasi-multipliers and embeddings of Hilbert $C^{*}$-bimodules, Can. J. Math. 46 (1994), 1150-1174. MR 95k:46091
  • [9] J.L. Garcia and J.J. Simon, Morita equivalence for idempotent rings, J. Pure Applied Algebra 76 (1991), 39-56. MR 93b:16010
  • [10] P. Green, Local structure of twisted covariant algebras, Acta Math. 140 (1978), 191-250. MR 58:12376
  • [11] G.G. Kasparov, Hilbert $C^{*}$-modules: Theorems of Stinespring and Voiculescu, J. Operator Theory 4 (1980), 133-150. MR 82b:46074
  • [12] S. Kyuno, Equivalence of module categories, Math J. Okayama Univ. 28 (1986), 147-150. MR 88e:16065
  • [13] E.C. Lance, Hilbert $C^{*}$-modules, Cambridge Univ. Press, LMS Lecture Note Series 210 Cambridge, 1995. MR 96k:46100
  • [14] A.J. Lazar and D.C. Taylor, Multipliers of Pedersen's ideal, Memoirs Amer. Math. Soc. 5 (1976). MR 54:944
  • [15] N. Nobusawa, $\Gamma $-rings and Morita equivalence of rings, Math. J. Okayama Univ. 26 (1984), 151-156. MR 86d:16048
  • [16] M. Parvathi and A. Ramakrishna Rao, Morita equivalence for a larger class of rings, Publ. Math. Debrecen 35 (1988), 65-71. MR 89m:16085
  • [17] G.K. Pedersen, $C^{*}$-algebras and their automorphism groups, Academic Press, London, 1979. MR 81e:46037
  • [18] N.C. Phillips, A new approach to the multipliers of Pedersen's ideal, Proc. Amer. Math. Soc. 104 (1988), 861-867. MR 89h:46081
  • [19] M.A. Rieffel, Induced representations of $C^{*}$-algebras, Advances in Math. 13 (1974), 176-257. MR 50:5489
  • [20] M.A. Rieffel, Morita equivalence for $C^{*}$-algebras and $W^{*}$-algebras, J. Pure Applied Algebra 5 (1974), 51-96. MR 51:3912
  • [21] M.A. Rieffel, Morita equivalence for operator algebras, Proc. Sym. Pure Math. 38, 285-298, Amer. Math. Soc., Providence, R.I., 1982. MR 84k:46045
  • [22] B. Stenstrom, Rings of Quotients, Springer-Verlag, 1975. MR 52:10782

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L08, 16D90

Retrieve articles in all journals with MSC (2000): 46L08, 16D90


Additional Information

Pere Ara
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
Email: para@mat.uab.es

DOI: https://doi.org/10.1090/S0002-9939-00-05688-4
Received by editor(s): March 30, 1998
Received by editor(s) in revised form: June 25, 1999
Published electronically: October 4, 2000
Additional Notes: This work was partially supported by DGYCIT and the Comissionat per Universitats i Recerca de la Generalitat de Catalunya
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society