Hypercyclic operators are operators with dense orbits. A contraction cannot be hypercyclic
since its orbits are bounded sets. Nevertheless, by multiplying a contraction with
a scalar of absolute value larger than 1, the resulting scaled contraction can occasionally
be a hypercyclic operator. In this paper, we investigate which Hilbert space contractions
have that property and which don't. We introduce the set Lambda(T) of all scalars
which produce a hypercyclic operator, by scaling the operator T, and determine Lambda(T)
in various cases. New properties of hyperciclic operators are discovered in this process.
For instance, it is proved that any connected component of the essential spectrum
of a hypercyclic operator must meet the unit circle.