A Numerical Radius Inequality for Hilbert-Schmidt Operators

In this paper, we prove that for every Hilbert-Schmidt operator T which acts on a Hilbert space r N/ r(T) <= root(2 - root 2)(||T||(2) (HS) rho(T)(2)), where rho(middot) , r(middot) and || middot ||HS denote spectral radius, numerical radius, and Hilbert- Schmidt norm, respectively.

Automated summary

In this paper, it is proven that for every Hilbert-Schmidt operator T in a Hilbert space, the inequality r(T) <= root(2 - root 2)(||T||(2) (HS) rho(T)(2)) holds, where rho(middot), r(middot), and || middot ||HS denote the spectral radius, numerical radius, and Hilbert-Schmidt norm, respectively.