Let
be the
set of all entire functions endowed with the topology of uniform convergence on compact
sets. Let
, let
be the composition
operator
,
and let
be the
derivative operator. We extend results on the hypercyclicity of the nonconvolution operators
by showing
that whenever
,
the collection of operators
forms an algebra under the usual addition and multiplication of operators which
consists entirely of hypercyclic operators (i.e., each operator has a dense orbit). We
also show that the collection of operators
consists entirely of hypercyclic operators.
|