Bull. Austral. Math. Soc. 72(2) pp.197--212, 2005.
On C*-algebras with the approximate n-th root property
A. Chigogidze |
A. Karasev |
K. Kawamura |
V. Valov |
The second author was partially supported by his NSERC
Grant 257231-04.
The paper was started during the third author's visit to Nipissing
University in July 2004.
The last author was partially supported by his NSERC Grant
261914-03.
Abstract
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 
> 0
there exists b
X such that |b| 1
and |a - bn|
< . 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.
2) if for every
a X
with |a| 1
and every > 0
there exists b
X such that |b| 1
and |a - bn|
< . 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 unitalC*-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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