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: Norm continuous group representations
Replies: 7   Last Post: Feb 18, 2008 11:17 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Julia Kuznetsova

Posts: 25
Registered: 3/14/07
Re: Norm continuous group representations
Posted: Feb 15, 2008 10:30 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> Can you produce an example where there is even one interesting
> operator-norm-continuous represenation?  I guess "interesting" would
> mean not essentially a direct sum of finite-dimensional
> representations.

Yes, the left regular representation of a discrete infinite group.
Similar action arises when G has two neighbourhoods of unity such that
VU\subset U. Then G acts norm-continuously on the subspace of L_2(G)
consisting of functions such that f(xU)=f(x) for all x.

I cannot think out less trivial examples, and this is why I'm asking
the question.

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.