On the numerical radius of weighted shifts on ${\ell }^2$ as a norm on ${\ell }^{\infty }$ and connections to Banach limits

Akram Sharif

We investigate the numerical radius of weighted shifts on ${\ell }^2$ as a norm on ${\ell }^{\infty }$. Along the way, we prove that the largest value a Banach limit can attain on the s…