Quasinormal operator

In functional analysis and operator theory, a **quasinormal operator** is a type of bounded linear operator on a Hilbert space that generalizes the concept of normal operators. An operator \( T \) on a Hilbert space \( H \) is called **normal** if it commutes with its adjoint, meaning \[ T^* T = T T^*, \] where \( T^* \) is the adjoint of \( T \).