On C*-algebras with the approximate n-th root property
2005 ◽
Vol 72
(2)
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pp. 197-212
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Keyword(s):
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.
1980 ◽
Vol 88
(3)
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pp. 425-428
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Keyword(s):
1994 ◽
Vol 123
(2)
◽
pp. 233-263
◽
Keyword(s):
2010 ◽
Vol 8
(2)
◽
pp. 167-179
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Keyword(s):
1959 ◽
Vol 11
◽
pp. 297-310
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