# Convexoid operator

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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 is spectraloid for every complex number .

## See also

## References

- T. Furuta.
*Certain convexoid operators*