This paper extends a
decomposition process of [Richard Arens, Operational calculus of linear relations,
Pacific J. Math., 11 (1961), 9–23] for closed linear relations, T, on a Hilbert space to
the setting in which T is a linear function from a dense linear subspace of a separable
normed linear complete space S1 to an innear product space S2. This decomposition
is used in showing that such a function contracted to a suitable dense linear
subspace of its initial set is the contraction of a closed linear function from a
dense linear subspace of S1 to S2. In particular, in case the initial set of
T is S1, it is shown that the contraction of T to a suitable dense linear
subspace of S1 is the contraction of a continuous linear function from S1 to
S2.
