𝐶*-algebras that are only weakly semiprojective

Loring, Terry

doi:10.1090/S0002-9939-98-04292-0

$C^\ast$-algebras that are only weakly semiprojective
HTML articles powered by AMS MathViewer

by Terry A. Loring PDF

Proc. Amer. Math. Soc. 126 (1998), 2713-2715 Request permission

Abstract:

We show that the $C^{*}$-algebra of continuous functions on the Cantor set is a weakly semiprojective $C^{*}$-algebra that is not semiprojective.

References

Bruce Blackadar, Shape theory for $C^\ast$-algebras, Math. Scand. 56 (1985), no. 2, 249–275. MR 813640, DOI 10.7146/math.scand.a-12100
S. Eilers, T. A. Loring and G. K. Pedersen Morphisms of extensions of $C^*$-algebras: pushing forward the Busby invariant, Adv. Math, to appear.
S. Eilers, T. A. Loring and G. K. Pedersen Stability of anticommutation relations. An application of noncommutative CW complexes, J. reine angew. Math., to appear.
E. G. Effros and J. Kaminker, Homotopy continuity and shape theory for $C^\ast$-algebras, Geometric methods in operator algebras (Kyoto, 1983) Pitman Res. Notes Math. Ser., vol. 123, Longman Sci. Tech., Harlow, 1986, pp. 152–180. MR 866493
Peter Friis and Mikael Rørdam, Almost commuting self-adjoint matrices—a short proof of Huaxin Lin’s theorem, J. Reine Angew. Math. 479 (1996), 121–131. MR 1414391, DOI 10.1515/crll.1996.479.121
H. Lin Homomorphisms from $C(X)$ into $C^{*}$-algebras, preprint.
Hua Xin Lin, Almost commuting unitary elements in purely infinite simple $C^*$-algebras, Math. Ann. 303 (1995), no. 4, 599–616. MR 1359951, DOI 10.1007/BF01461007
H. Lin Almost commuting self-adjoint matrices and applications, Operator Algebras and Their Applications, Fields Institute Communications, vol. 13, Amer. Math. Soc., Providence, RI, 1997, pp. 193–233.
J. C. Oxtoby and S. M. Ulam, On the existence of a measure invariant under a transformation, Ann. of Math. (2) 40 (1939), 560–566. MR 97, DOI 10.2307/1968940