Convexoid operator

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 [math]\displaystyle{ T - \lambda }[/math] is spectraloid for every complex number [math]\displaystyle{ \lambda }[/math].

See also

• Aluthge transform

References

• T. Furuta. Certain convexoid operators