Abstract. Let $S$ be a closed symmetric relation in a Hilbert space. If $S$ is densely defined, then the normal extensions of $S$ are selfadjoint. In general, normal nonselfadjoint intermediate extensions may not exist. Necessary and sufficient conditions for the existence of normal nonselfadjoint intermediate extensions are developed and all such extensions are parametrized.

DOI: 10.14232/actasm-013-008-0

AMS Subject Classification (1991): 47A06, 47B15, 47B25

Keyword(s): symmetric operator, symmetric relation, selfadjoint extension, normal extension

Received January 23, 2013, and in revised form February 21, 2013. (Registered under 8/2013.)