How I can start this problem?
$ X $ is unitary space. Prove that if $M_1, M_2 \subset X: $ $M_1\neq \emptyset ,M_2\neq \emptyset$ and $ M_1 \subset M_2 $ then $ M_2^\perp \subset M_1^\perp $
Thank you in advance
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What is a "unitary space"? Is it just an inner-product space? Also, what have you tried? Ultimately, this is a matter of bridging definitions with relatively straightforward manipulations. Are you having trouble with the definitions? – Ben Grossmann Apr 04 '16 at 18:39
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Directly (fill in details):
$$x\in M_2^\perp\implies \langle x,m_2\rangle=0\;,\;\forall\,m_2\in M_2\implies$$
this is true, in particular, for all $\;m_1\in M_1\subset M_2\implies x\in M_1^\perp\;$
DonAntonio
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