We estimate stable rank for $C^*$-tensor products with the Jiang-Su algebra.
We also estimate real rank for them as well.
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References
C. A. Akemann, G. K. Pedersen and J. Tomiyama, Multipliers of $C^*$-algebras, J. Funct. Anal., 13 (1973), 277--301.
Mathematical Reviews (MathSciNet):
MR470685
E. J. Beggs and D. E. Evans, The real rank of algebras of matrix valued functions, Internat. J. Math., 2 (1991), 131--138.
L. G. Brown and G. K. Pedersen, $C^*$-algebras of real rank zero, J. Funct. Anal., 99 (1991), 131--149.
X. Jiang and H. Su, On a simple unital projectionless $C^*$-algebra, Amer. J. Math., 121 (1999), 359--413.
Huaxin Lin, An introduction to the classification of amenable $C^*$-algebras, World Scientific, 2001.
M. Nagisa, H. Osaka and N. C. Phillips, Ranks of algebras of continuous $C^*$-algebra valued functions, Canad. J. Math., 53 (2001), 979--1030.
P. W. Ng and T. Sudo, On the stable rank of algebras of operator fields over an $n$-cube, Bull. London Math. Soc., 36 (2004), 358--364.
F. Perera and A. S. Toms, Recasting the Elliott conjecture, Math. Ann., 338 (2007), 669--702.
M. A. Rieffel, Dimension and stable rank in the $K$-theory of $C^*$-algebras, Proc. London Math. Soc., 46 (1983), 301--333.
Mathematical Reviews (MathSciNet):
MR693043
M. Rørdam, The stable and the real rank of $\mathcal Z$-absorbing $C^*$-algebras, Internat. J. Math., 15, no. 10 (2004), 1065--1084.
M. Rørdam and E. Størmer, Classification of Nuclear $C^*$-Algebras. Entropy in Operator Algebras, EMS 126 Operator Algebras and Non-Commutative Geometry VII, Springer, 2002.
T. Sudo, Real rank estimate by hereditary $C^*$-subalgebras by projections, Math. Scand., 100 (2007), 361--367.
A. S. Toms, On the independence of $K$-theory and stable rank for simple $C^*$-algebras, J. reine angew. Math., 578 (2005), 185--199.
N. E. Wegge-Olsen, K-theory and $C^*$-algebras, Oxford Univ. Press, 1993.