Square roots of complex symmetric operators

In this paper we study square roots of complex symmetric operators. In particular, we prove that if $ T{\in {\mathcal L}(\mathcal H)} $ T & ISIN;L(H) is a square root of a complex symmetric operator, then $ T<^>{\ast } $ T* has the single-valued extension property if and only if so does T. Moreover, in this case, T has the Bishop's property $ (\beta ) $ (beta) if and only if T is decomposable. Finally, we show that if T has a nontrivial hyperinvariant subspace, then $ T<^>{\ast } $ T* has a nontrivial invariant subspace.