Absorption and release of taste (בליעת טעם ופליטת טעם) occur when cooking non-kosher food in any utensil (except maybe glass).
Therefore, the utensils in a non-kosher kitchen, restaurant, or food production facility are surely themselves not kosher.
However, there is one leniency in this: taste is transferred between utensils and food, between utensils and liquids, but not between two utensils.
This opens the door for using a non-kosher stove or cooker to prepare your kosher meal.
As usual, sources are available through the links.