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Weakly compact homomorphisms from $ C\sp *$-algebras are of finite rank


Author: Martin Mathieu
Journal: Proc. Amer. Math. Soc. 107 (1989), 761-762
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1989-0998737-4
MathSciNet review: 998737
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Abstract: We give a straightforward proof of the fact that every weakly compact homomorphism from a $ {{\text{C}}^ * }$-algebra is a finite rank operator.


References [Enhancements On Off] (What's this?)

  • [1] S. B. Cleveland, Homomorphisms of non-commutative $ ^ * $-algebras, Pacific J. Math. 13 (1963), 1097-1109. MR 0158274 (28:1500)
  • [2] J. Galé, T. J. Ransford, Weakly compact homomorphisms of Banach algebras, preprint.
  • [3] F. Ghahramani, Compact homomorphisms of $ {C^ * }$-algebras, Proc. Amer. Math. Soc. 103 (1988), 458-462. MR 943066 (89e:46065)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0998737-4
Keywords: Weakly compact homomorphisms, $ {{\text{C}}^ * }$-algebras
Article copyright: © Copyright 1989 American Mathematical Society

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