  The paper is devoted to the problem of exact calculation of the norms in
ideal spaces for monotone operators on the cones of functions with monotonicity
properties. We implement a general approach to this problem that covers many
concrete variants of monotone operators in ideal spaces and different
monotonicity conditions for functions. As applications, we calculate the norms
of some integral operators on the cones, associate norms over some cones in
Lebesgue spaces, the norms of the dilation operator and embedding operators on
weighted Lorentz spaces with general weights. Under some more general
conditions, we present order sharp estimates for Hardy-type operators on the
cones.
