How can I determine if two eigenvectors form an open or closed subspace?

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Sergio Manzetti
Sergio Manzetti 2017-12-21
评论： Sergio Manzetti 2017-12-22
Hi, I have two eigenvectors, which form a subspace in H. Is there an easy way to determine whether the subspace they form is open or closed in H?
Thanks

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Torsten
Torsten 2017-12-21
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Matt J
Matt J 2017-12-21
编辑：Matt J 2017-12-21
From the document in Torsten's link,
"Every finite dimensional subspace of a Hilbert space H is closed."
The span of any two vectors is clearly an example of a finite dimensional sub-space and is therefore closed in L2.
Sergio Manzetti
Sergio Manzetti 2017-12-22
Thanks Matt. I take this is because they start from some point and are thus not infinite?

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