Graph-dense linear transformations
George O. Golightly · Pacific Journal of Mathematics · 1979
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 Si to an innear product space S 2 .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 Si to S 2 .In particular, in case the initial set of T is S l9 it is shown that the contraction of T to a suitable dense linear subspace of Si is the contraction of a continuous linear function from Si to S 2 .