Journal
COMPLEX ANALYSIS AND OPERATOR THEORY
Volume 17, Issue 2, Pages -Publisher
SPRINGER BASEL AG
DOI: 10.1007/s11785-023-01330-2
Keywords
Numerical radius; Spectral radius; Hilbert-Schmidt operator
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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.
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.
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