Define , (denoting the even part)
and
(denoting the odd part).
Then but
Assume W is a subspace of v.space V and that T is a linear operator.
Suppose that V = R(T) + W (DIRECT SUM) and W is T-Invariant.
Show by example that the conclusion for the thoerem if V IS FINITE-DIMENSIONAL THEN W = N(T) is not necessarily true if V is not finite dimensional...