KK-theory of reduced free-product $C^\ast$-algebras
Emmanuel Germain
Source: Duke Math. J. Volume 82, Number 3
(1996), 707-723.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077245258
Mathematical Reviews number (MathSciNet): MR1387690
Zentralblatt MATH identifier: 0863.46046
Digital Object Identifier: doi:10.1215/S0012-7094-96-08229-0
References
[1] D. Avitzour, Free products of $C\sp{\ast}$-algebras, Trans. Amer. Math. Soc. 271 (1982), no. 2, 423–435.
[2] B. Blackadar, $K$-theory for operator algebras, Mathematical Sciences Research Institute Publications, vol. 5, Springer-Verlag, New York, 1986.
Mathematical Reviews (MathSciNet): MR88g:46082
Zentralblatt MATH: 0597.46072
[3] J. Cuntz, $K$-theoretic amenability for discrete groups, J. Reine Angew. Math. 344 (1983), 180–195.
Mathematical Reviews (MathSciNet): MR86e:46064
Zentralblatt MATH: 0511.46066
Digital Object Identifier: doi:10.1515/crll.1983.344.180
[4] J. Cuntz, The $K$-groups for free products of $C\sp{\ast}$-algebras, Operator algebras and applications, Part I (Kingston, Ont., 1980), Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982, pp. 81–84.
Mathematical Reviews (MathSciNet): MR84f:46078
Zentralblatt MATH: 0502.46050
[5] E. Germain, $KK$-theory of reduced free product $C^{\ast}$- algebras with amalgamation over $C(X)$, Ph.D. dissertation, University of California at Berkeley, 1994.
Mathematical Reviews (MathSciNet): MR2691480
[6] P. Julg and A. Valette, $K$-theoretic amenability for ${\rm SL}\sb{2}({\bf Q}\sb{p})$, and the action on the associated tree, J. Funct. Anal. 58 (1984), no. 2, 194–215.
Mathematical Reviews (MathSciNet): MR86b:22030
Zentralblatt MATH: 0559.46030
Digital Object Identifier: doi:10.1016/0022-1236(84)90039-9
[7] G. Kasparov, Hilbert $C\sp{\ast}$-modules: theorems of Stinespring and Voiculescu, J. Operator Theory 4 (1980), no. 1, 133–150.
Mathematical Reviews (MathSciNet): MR82b:46074
Zentralblatt MATH: 0456.46059
[8] G. Kasparov, The operator $K$-functor and extensions of $C^{\ast}$-algebras, Mat. USSR Izv. 16 (1981), 513–572.
Zentralblatt MATH: 0464.46054
Mathematical Reviews (MathSciNet): MR582160
[9] E. Lance, $K$-theory for certain group $C\sp{\ast}$-algebras, Acta Math. 151 (1983), no. 3-4, 209–230.
Mathematical Reviews (MathSciNet): MR86f:46076
Zentralblatt MATH: 0542.46031
Digital Object Identifier: doi:10.1007/BF02393207
[10] K. McClanahan, $K$-theory for certain reduced free products of $C^{\ast}$-algebras, preprint, University of Mississippi, 1992.
[11] K. McClanahan, $KK$-group of crossed products by grouplike sets acting on trees, preprint, University of Mississippi, 1993.
[12] J. Mingo, On the contractibility of the unitary group of the Hilbert space over a $C\sp{\ast}$-algebra, Integral Equations Operator Theory 5 (1982), no. 6, 888–891.
Mathematical Reviews (MathSciNet): MR84c:58008
Zentralblatt MATH: 0494.46064
Digital Object Identifier: doi:10.1007/BF01694068
[13] M. Pimsner, $KK$-groups of crossed products by groups acting on trees, Invent. Math. 86 (1986), no. 3, 603–634.
Mathematical Reviews (MathSciNet): MR88f:22022
Zentralblatt MATH: 0638.46049
Digital Object Identifier: doi:10.1007/BF01389271
[14] M. Pimsner and D. Voiculescu, $K$-groups of reduced crossed products by free groups, J. Operator Theory 8 (1982), no. 1, 131–156.
Mathematical Reviews (MathSciNet): MR84d:46092
Zentralblatt MATH: 0533.46045
[15] J. Rosenberg and C. Schochet, The Künneth theorem and the universal coefficient theorem for Kasparov's generalized $K$-functor, Duke Math. J. 55 (1987), no. 2, 431–474.
Mathematical Reviews (MathSciNet): MR88i:46091
Zentralblatt MATH: 0644.46051
Digital Object Identifier: doi:10.1215/S0012-7094-87-05524-4
Project Euclid: euclid.dmj/1077306030
[16] G. Skandalis, Une notion de nucléarité en $K$-théorie (d'après J. Cuntz), $K$-Theory 1 (1988), no. 6, 549–573.
Mathematical Reviews (MathSciNet): MR90b:46131
Zentralblatt MATH: 0653.46065
Digital Object Identifier: doi:10.1007/BF00533786
[17] G. Skandalis, Kasparov's bivariant $K$-theory and applications, Exposition. Math. 9 (1991), no. 3, 193–250.
Mathematical Reviews (MathSciNet): MR92h:46101
Zentralblatt MATH: 0746.19008
[18] E. H. Spanier, Algebraic topology, Springer-Verlag, New York, 1981, corrected reprint.
Mathematical Reviews (MathSciNet): MR83i:55001
Zentralblatt MATH: 0477.55001
[19] D. Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), no. 1, 97–113.
Mathematical Reviews (MathSciNet): MR54:3427
Zentralblatt MATH: 0335.46039
[20] D. Voiculescu, Symmetries of some reduced free product $C\sp \ast$-algebras, Operator algebras and their connections with topology and ergodic theory (Buşteni, 1983), Lecture Notes in Math., vol. 1132, Springer, Berlin, 1985, pp. 556–588.
Mathematical Reviews (MathSciNet): MR87d:46075
Zentralblatt MATH: 0618.46048
Digital Object Identifier: doi:10.1007/BFb0074909
[21] D. Voiculescu, The $K$-groups of the $C\sp *$-algebra of a semicircular family, $K$-Theory 7 (1993), no. 1, 5–7.
Mathematical Reviews (MathSciNet): MR94f:46093
Zentralblatt MATH: 0786.46054
Digital Object Identifier: doi:10.1007/BF00962789
Duke Mathematical Journal
