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Exercise 3.F.21

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Proof. We will prove the contrapositive.

Suppose that $U ⊄ W$ . Use the notation from _Theorem 1_ in Chapter 2 notes. We have that $ψ_{1} \in W^{0}$ , but $ψ_{1} \notin U^{0}$ (because of linear independence with the basis of $U^{0}$ ), hence $W^{0} ⊄ U^{0}$ . □

celiopassos

2017-10-06 00:00

Exercise 3.F.21

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