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Approximating maps and exact C*-algebras

Published online by Cambridge University Press:  24 October 2008

R. J. Archbold
Affiliation:
University of Aberdeen

Extract

Let A and E be C*-algebras, let AB denote the minimal C*-tensor product, and let ε A *. The right slice map R: ABB is the unique bounded linear mapping with the property that R (ab) = (a)b (a ε A, b ε B)(10). A triple (A, B, D), where D is a C*-subalgebra of B, is said to have the slice map property if whenever x ε AB and R(x) D for all ε A* then x ε AD). It is known that (A, B, D) has the slice map property whenever A is nuclear (11,13), but it appears to be still unknown whether the nuclearity of B will suffice (unless some extra condition is placed on D (l)).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

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