The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math.research

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: quasi-central nets in C*-algebras
Replies: 1   Last Post: Aug 8, 2017 8:39 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View

Posts: 31
Registered: 2/23/09
Re: quasi-central nets in C*-algebras
Posted: Aug 8, 2017 8:39 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Does this follow from prop II.8.1.5 (p. 165) in
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)
||a(c_alpha) - (c_alpha)a|| < ||a||(delta)

On Monday, July 31, 2017 at 3:15:34 PM UTC-6, 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.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.