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

Published online by Cambridge University Press:  17 April 2009

A. Chigogidze ,
A. Karasev ,
K. Kawamura  and
V. Valov
A. Chigogidze
Affiliation:
Department of Mathematical Sciences, University of North Carolina at Greensboro, P.O. Box 26170, Greensboro, NC 27402–6170, United States of America e-mail: chigogidze@uncg.edu
A. Karasev
Affiliation:
Department of Computer Science and Mathematics, Nipissing University, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada e-mail: alexandk@nipissingu.ca
K. Kawamura
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305–8071, Japan e-mail: kawamura@math.tsukuba.as.jp
V. Valov
Affiliation:
Department of Computer Science and Mathematics, Nipissing University, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada e-mail: veskov@nipissingu.ca
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We say that a C*-algebra X has the approximate n-th root property (n ≥ 2) if for every a ∈ X with ∥a∥ ≤ 1 and every ɛ > 0 there exits b ∈ X 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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 2 , October 2005 , pp. 197 - 212
Copyright
Copyright © Australian Mathematical Society 2005

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