In this paper we study square roots of complex symmetric operators. In particular, we prove that if (Formula presented.) is a square root of a complex symmetric operator, then (Formula presented.) has the single-valued extension property if and only if so does T. Moreover, in this case, T has the Bishop's property (Formula presented.) if and only if T is decomposable. Finally, we show that if T has a nontrivial hyperinvariant subspace, then (Formula presented.) has a nontrivial invariant subspace.
- Square roots of complex symmetric operators
- nontrivial invariant subspace
- the Bishop's property
- the Dunford's property (C)
- the dunford's boundedness condition (B)
- the single-valued extension property