Fractional powers of dissipative operators

A is closed and maximal accretive, A^ and A^* are comparable for 0<1/2 ; by this we mean that A^t and A^* have the same domain D₀ and that the ratios A^*u/ A^au for u D₀ are bounded from above and from below by positive constants. Another result is that A^ and A^* have an acute angle for 0<1/2 ; by this is meant that Re (A^au, A^*u) / A^au A^*u 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 H₀= (A^a+A^*) /2 is nonnegative self- adjoint and that it is comparable, and has acute angle, with both A^a and