Abstract: This paper deals, constructively, with two theorems on the sequential continuity of linear mappings. The classical proofs of these theorems use the boundedness of the linear mappings, which is a constructively stronger property than sequential continuity; and constructively inadmissable versions of the Banach-Steinhaus theorem.

In classical operator theory it is taken for granted that we can project onto the closure of the range of an operator T on a Hilbert space H. In a constructive development of operator theory, to which this note is a contribution, this projection exists if and only if ran(r), the range of T, is located, in the sense that the distance