Does this follow from prop II.8.1.5 (p. 165) in
http://wolfweb.unr.edu/homepage/bruceb/Cycr.pdf
?
Applied once for each (a, alpha, epsilon > 0) with X := the closed real interval [0, ||c_alpha||], and f(x) := sqrt(x) to obtain:
There exists delta > 0 with
||a((c_alpha)^(1/2)) - ((c_alpha)^(1/2))a|| < ||a||(epsilon)
whenever
||a(c_alpha) - (c_alpha)a|| < ||a||(delta)
On Monday, July 31, 2017 at 3:15:34 PM UTC-6,
vru...@ualberta.ca wrote:
Dear all,
Let's call a net ( c_\alpha )_\alpha in a C^* algebra A quasi-central if
a c_\alpha - c_\alpha a \to 0 for each a in A.
Suppose that all c_\alphas are non-negtative (so that
c_\alpha^\frac{1}{2} exists for each \alpha). Is then the net ( c_\alpha^\frac{1}{2} )_\alpha in A also quasi-central. If ( c_\alpha
)_\alpha is bounded, the answer is easily seen to be true by Gelfand
theory, but what about the unbounded case?
Thanks for any hints!
Volker Runde.
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)