newtonian mechanics - Is the coefficient of restitution frame independent and energy conservation?

In this question I am ignoring relativistic effects. The following statements I think are true:

1. change in Kinetic energy is not invariant under change of frame


2. Force is invariant under change in frame


3. Change in velocity and relative velocity between two particles is invariant under change of frame


4. The coefficient of restitution is given by $e=|\frac{v_1-v_2}{u_1-u_2}|=\sqrt{1-\frac{\Delta E}{T'}}$ where $\Delta E$ is the change in kinetic energy in the frame we are in and $T'$ is the initial kinetic energy in the centre of mass frame.

So here is my problem. If 2. is correct work done is invariant and therefore from the work energy theorem 1. must be wrong (since w.d=change in kinetic energy). If both 1 and 3 are right then 4. must be wrong as the first equation for e would stay the same under change of frame whilst the second would change. Please can you explain which of these expressions is wrong, thanks.

Answer

The first statement is wrong. The total energy of a body changes with frame but the change in kinetic energy does not. It is constant. This statement can also be viewed as the fact that conservation of energy is valid on all inertial frames.