ON COMMUTATIVE AND NON-COMMUTATIVE C-ALGEBRAS WITH THE APPROXIMATE n-TH ROOT PROPERTY
نویسنده
چکیده
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 ε > 0 there exits b ∈ X such that ‖b‖ ≤ 1 and ‖a − bn‖ < ε. Some properties of commutative and non-commutative C∗-algebras having the approximate nth root property are investigated. In particular, it is shown that there exists a non-commutative (resp., 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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