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A topological characterisation of finite dimensionality of C* -algebras

Published online by Cambridge University Press:  17 April 2009

Wai-Shing Tang
Wai-Shing Tang
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge, Republic of Singapore 0511
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Abstract

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A C*-algebra A is finite-dimensional if and only if the cone is closed in M2 ⊗ A.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 3 , December 1988 , pp. 329 - 333
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Choi, M. -D., ‘Positive linear maps’, Proc. Sympos. Pure Math. 38 (1982), 583–590.CrossRefGoogle Scholar
[2]Ogasawara, T., ‘Finite dimensionality of certain Banach algebras’, J. Sci. Hiroshima Univ. Ser. A. 17 (1954), 359–364.Google Scholar
[3]Rudin, W., Functional Analysis (McGraw-Hill, New York, 1973).Google Scholar
[4]Smith, R.R., ‘Completely bounded maps between C*-algebras’, J. London Math. Soc. (2) 27 (1983), 157–166.CrossRefGoogle Scholar
[5]Takesaki, M., Theory of Operator Algebras I (Springer Verlag, Berlin, 1979).CrossRefGoogle Scholar