On the Kato square root problem

Abstract

In the infinite-dimensional separable complex Hilbert space we construct new abstract examples of unbounded maximal accretive and maximal sectorial operators $B$ for which $\mathrm{dom}{B}^{\frac{1}{2}}\ne \mathrm{dom}{B}^{\ast \frac{1}{2}}$. New criterions for the equality are established.