Abstract. We give characterization for the range and the domain of the square root of smallest (Krein--von Neumann) and largest (Friedrichs) positive self-adjoint extension of an operator. In the last theorem we give range characterization for the square root of the largest positive extension of smallest possible norm, if bounded positive extension exists.

AMS Subject Classification (1991): 47A05, 47A20, 47B25

Keyword(s): Krein--von Neumann, Friedrichs extension

Received May 6, 1996 and in revised form September 11, 1996. (Registered under 6130/2009.)