| Inspired by a statement of W. Luh asserting the
existence of entire functions having together
with all their derivatives and antiderivatives
some kind of additive universality or
multiplicative universality on certain compact
subsets of the complex plane or of, respectively,
the punctured complex plane, we introduce in this
paper the new concept of U-operators, which are
defined on the space of entire functions.
Concrete examples, including differential and
antidifferential operators, composition,
multiplication and shift operators, are studied.
A result due to Luh, Martirosian and Müller
about the existence of universal entire functions
with gap power series is also strengthened.