Thread: Someone PLEASEEE answer this T-INVARIANT QUESTION

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...

Define , (denoting the even part)

and
(denoting the odd part).

Then but

My previous answer is SO WRONG!!

Must be careful what I say henceforth...

Try the map defined by