Some inequalities for $(α, β)$-normal operators in Hilbert spaces

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159915An operator $T$ acting on a Hilbert space is called $(α,β)$-normal ($0\leq α\leq 1\leq β$) if \begin{equation*} α^{2}T^{\ast }T\leq TT^{\ast}\leq β^{2}T^{\ast}T. \end{equation*} In this paper we establish various inequalities between the operator norm and its numerical radius of $(α,β)$-normal operators in Hilbert spaces. For this purpose, we employ some classical inequalities for vectors in inner product spaces.11 pagesFunctional AnalysisOperator Algebras47A12Some inequalities for $(α, β)$-normal operators in Hilbert spacestext