On the square roots of strictly quasiaccretive complex matrices

The square roots of a complex n×n matrix A for which the real part of e^ixA, where $\text{χ?[}\text{?π}\text{2}\text{,}\text{π}\text{2}\text{]}$, is positive definite are investigated. It is shown, for example, that when $\text{χ=}\text{?π}\text{2}$ (i.e., A is strictly dissipative), A has a unique square root whose real and imaginary parts are both positive definite.