Let's see if I succeed in decoding the above: T,U are linear operators and N(T), N(U) are the corresponding null spaces, or kernel, of these operators.

So, if then .

Assuming I guessed correctly your symbols, the claim is false: as example take ,

It's easy to check that , but , as you can easily check.

If by the above symbols you meant something else then the above is worthless (perhaps the above's worthless EVEN if I guessed correctly your symbols).

Tonio