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Morita equivalence and Pedersen ideals

Author(s): Pere Ara
Journal: Proc. Amer. Math. Soc. 129 (2001), 1041-1049.
MSC (2000): Primary 46L08, 16D90
Posted: October 4, 2000
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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:

[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

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Additional Information:

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

DOI: 10.1090/S0002-9939-00-05688-4
PII: S 0002-9939(00)05688-4
Received by editor(s): March 30, 1998
Received by editor(s) in revised form: June 25, 1999
Posted: 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
Copyright of article: Copyright 2000, American Mathematical Society

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