Complex symmetric partial isometries

An operator T ∈ B(H) is complex symmetric if there exists a conjugate-linear, isometric involution C :H→H so that T = CT ∗C.We provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial isometry on a Hilbert space of dimension 4 is complex symmetric. © 2009 Elsevier Inc. All rights reserved