Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: quasicentral nets in C*algebras
Posted:
Aug 8, 2017 8:39 AM


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 UTC6, vru...@ualberta.ca wrote: > Dear all, > > Let's call a net ( c_\alpha )_\alpha in a C^* algebra A quasicentral if > > a c_\alpha  c_\alpha a \to 0 for each a in A. > > Suppose that all c_\alphas are nonnegtative (so that > c_\alpha^\frac{1}{2} exists for each \alpha). Is then the net ( > c_\alpha^\frac{1}{2} )_\alpha in A also quasicentral. 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.



