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On C*-algebras with the approximate n-th root property

  • A. Chigogidze (a1), A. Karasev (a2), K. Kawamura (a3) and V. Valov (a4)
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We say that a C*-algebra X has the approximate n-th root property (n2) if for every aX with ∥a∥ ≤ 1 and every ɛ > 0 there exits bX such that ∥b∥ ≤ 1 and ∥a − bn∥ < ɛ. Some properties of commutative and non-commutative C*-algebras having the approximate n-th root property are investigated. In particular, it is shown that there exists a non-commutative (respectively, commutative) separable unital C*-algebra X such that any other (commutative) separable unital C*-algebra is a quotient of X. Also we illustrate a commutative C*-algebra, each element of which has a square root such that its maximal ideal space has infinitely generated first Čech cohomology.

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References
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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