I am studying Functional analysis.
And I don't understand an equation that is followed as below :
If $S_1$ and $S_2$ are vector spaces, then $(S_1 \otimes S_2)^\perp = (S_1 ^\perp \otimes S_2) + (S_1 \otimes S_2 ^\perp) + (S_1 ^\perp \otimes S_2 ^\perp)$
Clearly, the left side contains the right side. But I don't have any idea that makes the reverse containment is possible.
If anyone shows that the right side contains the left one, I will really appreciated.
Thanks a lot before!