Abstract
This survey article describes the connection between the theory of generalized inductive limits of finite-dimensional C*-algebras and quasidiagonality. Connections with the classification problem for separable nuclear C*-algebras are also discussed.
Supported by NSF grant DMS-9706982
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References
B. Blackadax, K-Theory for Operator Algebras. Second Edition, Cambridge University Press, 1998.
B. Blackadar and E. Kirchberg, Generalized inductive limits of finitedimensional C*-algebras, Math. Ann. 307 (1997), 343–380.
B. Blackadar and E. Kirchberg, Inner quasidiagonality and strong NF algebras, to appear in Pacific J. Math.
B. Blackadar and E. Kirchberg, Irreducible representations of inner quasidiagonal C*-algebras, to appear.
L.Brown,The universal coefficient theorem for Ext and quasidiagonality, in Operator Algebras and Group Representations, Pitman, Boston/London/Melbourne, 1983.
L. Brown and M. Dadarlat, Extensions of C*-algebras and quasidiagonality, J. London Math. Soc. 53 (1996), 582–600.
M.-D. Choi and E. Effros, Injectivity and operator spaces, J. Fund. Anal.24 (1977), 156–209.
M. Dadarlat, Residually finite-dimensional C*-algebras. Operator Algebras and Operator Theory (Shanghai 1997), Contemp. Math. 228, American Mathematical Society, 1998.
M. Dadarlat and S. Eilers, Approximate homogeneity is not a local property, J. Reine Angew. Math. 507 (1999), 1–13.
M. Dadarlat and T. Loring, Extensions of certain real rank zero C*-algebras, Ann. Inst. Fourier (Grenoble) 44 (1994), 907–925.
K. Davidson, D. Herrero, and N. Salinas, Quasidiagonal operators, approximation and C*-algebras, Indiana Univ. Math. J. 38 (1989), 973–998.
M. Gromov, Hyperbolic groups. In Essays in Group Theory, MSRI Publications 8, Springer-Verlag, 1987.
P. Halmos, A Hilbert Space Problem Book, Graduate Texts in Mathematics 19, Springer-Verlag, 1982.
J. Rosenberg and C. Schochet, The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized K-functor, Duke Math. J. 55 (1987), 431–474.
J. Spielberg, Embedding C*-algebra extensions into AF algebras, J. Functional Anal. 81 (1989), 325–344.
D. Voiculescu, A noncommutative Weyl-von Neumann theorem, Rev. Roum. Math. Pures Appl. 21 (1976), 97–113.
D. Voiculescu, A note on quasidiagonal C*-algebras and homotopy, Duke Math. J. 62 (1991), 267–272.
D. Voiculescu, Around quasidiagonal operators, Integral Equations Operator Theory 17 (1993), 137–149.
S. Wassermann, C*-Algebras associated with groups with Kazhdan’s property T, Ann. of Math. 134 (1991), 423–431.
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Blackadar, B., Kirchberg, E. (2000). Generalized Inductive Limits and Quasidiagonality. In: Cuntz, J., Echterhoff, S. (eds) C*-Algebras. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57288-3_2
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DOI: https://doi.org/10.1007/978-3-642-57288-3_2
Publisher Name: Springer, Berlin, Heidelberg
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