Equivariant triviality theorems for Hilbert $C^{\ast }$-modules
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- by J. A. Mingo and W. J. Phillips PDF
- Proc. Amer. Math. Soc. 91 (1984), 225-230 Request permission
Abstract:
The purpose of this paper is to give an exposition of the various triviality theorems, the equivariant version of a result due to L. Brown, and a simplification of the proof of Kasparov’s triviality theorems.References
- Johan F. Aarnes and Richard V. Kadison, Pure states and approximate identities, Proc. Amer. Math. Soc. 21 (1969), 749–752. MR 240633, DOI 10.1090/S0002-9939-1969-0240633-1
- Lawrence G. Brown, Stable isomorphism of hereditary subalgebras of $C^*$-algebras, Pacific J. Math. 71 (1977), no. 2, 335–348. MR 454645
- Lawrence G. Brown, Philip Green, and Marc A. Rieffel, Stable isomorphism and strong Morita equivalence of $C^*$-algebras, Pacific J. Math. 71 (1977), no. 2, 349–363. MR 463928
- Jacques Dixmier, $C^*$-algebras, North-Holland Mathematical Library, Vol. 15, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Translated from the French by Francis Jellett. MR 0458185
- Jacques Dixmier and Adrien Douady, Champs continus d’espaces hilbertiens et de $C^{\ast }$-algèbres, Bull. Soc. Math. France 91 (1963), 227–284 (French). MR 163182
- Maurice J. Dupré and Peter A. Fillmore, Triviality theorems for Hilbert modules, Topics in modern operator theory (Timişoara/Herculane, 1980), Operator Theory: Advances and Applications, vol. 2, Birkhäuser, Basel-Boston, Mass., 1981, pp. 71–79. MR 672817
- G. G. Kasparov, Hilbert $C^{\ast }$-modules: theorems of Stinespring and Voiculescu, J. Operator Theory 4 (1980), no. 1, 133–150. MR 587371
- G. G. Kasparov, The operator $K$-functor and extensions of $C^{\ast }$-algebras, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), no. 3, 571–636, 719 (Russian). MR 582160 —, $K$-theory, group ${C^ * }$-algebras, and higher signatures. Part I, Conspectus. Chernogolovka, 1981 (preprint).
- Marc A. Rieffel, Induced representations of $C^{\ast }$-algebras, Advances in Math. 13 (1974), 176–257. MR 353003, DOI 10.1016/0001-8708(74)90068-1
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 225-230
- MSC: Primary 46L05; Secondary 46M20
- DOI: https://doi.org/10.1090/S0002-9939-1984-0740176-0
- MathSciNet review: 740176