Linear extensions of relations between vector spaces
Let and be vector spaces over the same field . Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation of into is called linear if and for all and . After improving and supplementing some former results on linear relations, we show that a relation of a linearly independent subset of into can be extended to a linear relation of into if and only if there exists a linear subspace of such that for all . Moreover, if generates...