Abstract. This note is the counterpart of [1] in which it was given a new contruction of the smallest positive self-adjoint extension of a positive linear map. In this note we apply this method to the largest positive self-adjoint extension, and we prove a sufficient condition for a pair of bounded operators to be interwined by this extension.

AMS Subject Classification (1991): 47A20, 47B25

Keyword(s): Friedrichs extension, commutation

Received October 12, 1995. (Registered under 5722/2009.)