Re: State on classical space

Re: State on classical space

Following your ideas, |w(f)| < 4(pi)^2 ||f|| where the last norm is the one in your space so what about v(f)=w(f)/4(pi)^2?

Re: State on classical space

I don't think that will work. It will be fine for that particular function, but we can just as well consider a function that maps any element of the torus to say 2, then the integral will have twice that value. I think I have an idea how to construct such a state, will post it if it works.

Re: State on classical space

I was assuming there was a typo in your definition of the norm of the functional since by linearity that quantity will never be bounded. So I assumed you meant $\displaystyle \| \omega \| = \sup_{\| f \| =1} |\omega (f)|$ and for this definition my example does work.