Operators characterized by certain Cauchy-Schwarz type inequalities
Operators characterized by certain Cauchy-Schwarz type inequalities
A Hilbert space operator T satisfying \begin{align*} &\text{either } && (**) && |(T ΞΎ, Ξ·)|^2 β€ (|T| _ΞΎ,ΞΎ) (|T| _Ξ·,Ξ·)\ \text{for all } ΞΎ, Ξ·\in \mathcal H, \\ &\text{or } && (*) && |(T ΞΎ, ΞΎ)| β€ (|(T|_ΞΎ,ΞΎ) \ \text{for all } ΞΎ\in \mathcal H, \end{align*} is studied. The condition β¦