In mathematics, especially operator theory, a convexoid operator is a bounded linear operator T on a complex Hilbert space H such that the closure of the numerical range coincides with the convex hull of its spectrum. An example of such an operator is a normal operator (or some of its generalization). A closely related operator is a spectraloid operator: an operator whose spectral radius coincides with its numerical radius. In fact, an operator T is convexoid if and only if T − λ {\displaystyle T-\lambda } is spectraloid for every complex number λ {\displaystyle \lambda } .
See also Aluthge transform
References T. Furuta. Certain convexoid operators