  We shall consider a stochastic maximum principle of optimal control for a
control problem associated with a stochastic partial differential equations of
the following type:
  d x(t) = (A(t) x(t) + a (t, u(t)) x(t) + b(t, u(t)) dt + [<\sigma(t, u(t)),
x(t)>_K + g (t, u(t))] dM(t),
  x(0) = x_0 \in K,
  with some given predictable mappings $a, b, \sigma, g$ and a continuous
martingale $M$ taking its values in a Hilbert space $K,$ while $u(\cdot)$
represents a control. The equation is also driven by a random unbounded linear
operator $A(t,w), \; t \in [0,T ], $ on $K .$ We shall derive necessary
conditions of optimality for this control problem without a convexity
assumption on the control domain, where $u(\cdot)$ lives, and also when this
control variable is allowed to enter in the martingale part of the equation.
