Abstract
The numerical range and numerical radius of some model operators are investigated. Among other things, a complete description of the numerical range of square-zero operators on Hilbert spaces, including the skew-symmetric Volterra operator
(
V
0
f
)
(
x
)
=
∫
-
x
x
f
(
t
)
dt
on the Lebesgue space
L
2
(
-
1
,
1
)
,
is also given.