Tokyo Journal of Mathematics

Stable Rank for $C^*$-tensor Products with the Jiang-Su Algebra

Takahiro SUDO

Source: Tokyo J. of Math. Volume 32, Number 1 (2009), 19-26.

Abstract

We estimate stable rank for $C^*$-tensor products with the Jiang-Su algebra. We also estimate real rank for them as well.

Primary Subjects: 46L05
Secondary Subjects: 46L80

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.tjm/1249648406
Digital Object Identifier: doi:10.3836/tjm/1249648406
Zentralblatt MATH identifier: 05604232
Mathematical Reviews number (MathSciNet): MR2541151

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
Digital Object Identifier: doi:10.1016/0022-1236(73)90036-0
E. J. Beggs and D. E. Evans, The real rank of algebras of matrix valued functions, Internat. J. Math., 2 (1991), 131--138.
Mathematical Reviews (MathSciNet): MR1094700
Zentralblatt MATH: 0748.46030
Digital Object Identifier: doi:10.1142/S0129167X91000089
L. G. Brown and G. K. Pedersen, $C^*$-algebras of real rank zero, J. Funct. Anal., 99 (1991), 131--149.
Mathematical Reviews (MathSciNet): MR1120918
Zentralblatt MATH: 0776.46026
Digital Object Identifier: doi:10.1016/0022-1236(91)90056-B
X. Jiang and H. Su, On a simple unital projectionless $C^*$-algebra, Amer. J. Math., 121 (1999), 359--413.
Mathematical Reviews (MathSciNet): MR1680321
Zentralblatt MATH: 0923.46069
Digital Object Identifier: doi:10.1353/ajm.1999.0012
Huaxin Lin, An introduction to the classification of amenable $C^*$-algebras, World Scientific, 2001.
Mathematical Reviews (MathSciNet): MR1884366
Zentralblatt MATH: 1013.46055
M. Nagisa, H. Osaka and N. C. Phillips, Ranks of algebras of continuous $C^*$-algebra valued functions, Canad. J. Math., 53 (2001), 979--1030.
Mathematical Reviews (MathSciNet): MR1859764
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.
Mathematical Reviews (MathSciNet): MR2038723
Zentralblatt MATH: 1066.46046
Digital Object Identifier: doi:10.1112/S0024609303002881
F. Perera and A. S. Toms, Recasting the Elliott conjecture, Math. Ann., 338 (2007), 669--702.
Mathematical Reviews (MathSciNet): MR2317934
Zentralblatt MATH: 1161.46035
Digital Object Identifier: doi:10.1007/s00208-007-0093-3
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
Zentralblatt MATH: 0533.46046
Digital Object Identifier: doi:10.1112/plms/s3-46.2.301
M. Rørdam, The stable and the real rank of $\mathcal Z$-absorbing $C^*$-algebras, Internat. J. Math., 15, no. 10 (2004), 1065--1084.
Mathematical Reviews (MathSciNet): MR2106263
Zentralblatt MATH: 1077.46054
Digital Object Identifier: doi:10.1142/S0129167X04002661
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.
Mathematical Reviews (MathSciNet): MR1878883
T. Sudo, Real rank estimate by hereditary $C^*$-subalgebras by projections, Math. Scand., 100 (2007), 361--367.
Mathematical Reviews (MathSciNet): MR2339373
Zentralblatt MATH: 1161.46031
A. S. Toms, On the independence of $K$-theory and stable rank for simple $C^*$-algebras, J. reine angew. Math., 578 (2005), 185--199.
Mathematical Reviews (MathSciNet): MR2113894
N. E. Wegge-Olsen, K-theory and $C^*$-algebras, Oxford Univ. Press, 1993.
Mathematical Reviews (MathSciNet): MR1222415
Zentralblatt MATH: 0780.46038

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