Abstract
Let be a complex Hilbert space and let
be the set of all bounded linear operators on
. For every
, the joint numerical radius of
is denoted by
. We give a description for surjective mappings
such that
for all
, when
is infinite-dimensional. This complements a recent result of Li and Poon for such mappings when
is finite-dimensional. We also study the Davis–Wielandt radius,
, of
. A description for surjective mappings
such that
for all
is also given.