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 \( {\displaystyle T-\lambda } \) is spectraloid for every complex number\( \lambda \).
See also
Aluthge transform
References
T. Furuta. Certain convexoid operators
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
