  We consider the optimal control problem of stochastic evolution equations in
a Hilbert space under a recursive utility, which is described as the solution
of a backward stochastic differential equation (BSDE). A very general maximum
principle is given for the optimal control, allowing the control domain not to
be convex and the generator of the BSDE to vary with the second unknown
variable $z$. The associated second-order adjoint process is characterized as a
unique solution of a conditionally expected operator-valued backward stochastic
integral equation.
