The closure of a similarity orbit is always arcwise connected

If T, A are Hilbert space operators such that A is the norm-limit of operators similar to T, then there exists a continuous function from 0,1] into the algebra of operators such that (t) is a limit of similarities of T for all t in the interval 0,1], (0)=T and (1)=A.This research was partially supported by a Grant of the National Science Foundation.