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.
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