The elliptical range theorem for the conformal range

The conformal range (or the real Davis–Wielandt shell), which is a particular planar projection of the Davis–Wielandt shell, can be considered as the hyperbolic version of the numerical range; i. e. it is a ``field of values’’ which can be interpreted as a subset of the asymptotically closed hyperbolic plane. Here we explain the analogue of the elliptical range theorem of $2\times 2$ complex matrices for the conformal range.