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

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Julia Kuznetsova

Posts: 25
Registered: 3/14/07
Re: Norm continuous group representations
Posted: Feb 15, 2008 10:30 AM
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> 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.




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