Fractional powers of dissipative operators

A$ is closed and maximal accretive, $Aα$ and $A*α$ are comparable for $0α<1/2$ ; by this we mean that $Aᵗ$ and $A*α$ have the same domain $Dₐ$ and that the ratios $ A*αu/ Aᵃu$ for $u∈ Dₐ$ are bounded from above and from below by positive constants.Another result is that $Aα$ and $A*α$ have an acute angle for $0α<1/2$ ; by this is meant that ${ Re}(Aᵃu, A*αu)/ Aᵃu A*αu$ is bounded from below by a positive constant (see Sobolevskii [17]).These results are remarkable in view of the fact that nothing is assumed for the relationship between the domains of $A$ and $A*$ themselves or for the angle between $A$ and $A*$ .It follows from these results that $Hₐ=(Aᵃ+A*α)/2$ is nonnegative self- adjoint and that it is comparable, and has acute angle, with both $Aᵃ$ and