On the (U+K)-orbits of certain weighted shifts

D. A. Herrero has defined the (U+K)-orbit of an operatorT acting on an Hilbert space as (U+K)(T)={R ^–1 TR: R invertible of the form unitary plus compact}. In this paper we consider the (U+K)-orbit and the closure thereof for bilateral and unilateral weighted shifts. In particular, we determine which shifts are in the (U+K)-orbits of injective weighted shifts and which shifts are in the closure of the (U+K)-orbit of periodic injective shifts. Also, the closure of the (U+K)-orbit of injective essentially normal shifts is determined.Research supported in part by an NSERC operating grant.