Abstract. We introduce a topology in the set of all semiclosed operators in a Hilbert space and investigate the topological structure by using the method of quotients of bounded operators. Under our topology, it is shown that the set of all closed operators is open in the set of all semiclosed operators, and that the topology restricted to the set of all closed operators is strictly stronger than the topology induced from the gap metric.

AMS Subject Classification (1991): 47A65

Keyword(s): semiclosed operators, quotients of bounded operators, semiclosed subspaces

Received April 4, 2005, and in revised form December 11, 2006. (Registered under 5967/2009.)