Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 0 down vote favorite

I have read in proofwiki that a direct sum of Hilbert spaces is a Hilbert space. However, Wikipedia Page about direct sum says it is not necessarily true, that is, the direct sum of Hilbert spaces is not always a complete space. Which of them is right? In what Conditions the direct sum of Hilbert spaces is a Hilbert space?

share|improve this question
3  
Note that proofwiki uses what they call the "Hilbert space direct sum" which is what Wikipedia describes in the relevant section a few lines later, starting with "Alternatively and equivalently ..." – t.b. Sep 16 '12 at 16:22
But Wikipédia presents a condition that is not present on proofwiki: the sum of all norms for each function on the direct sum must converge. – user38397 Sep 16 '12 at 16:32
2  
No, as usual proofwiki is terribly written, but they impose that condition, too: proofwiki.org/wiki/Definition:Hilbert_Space_Direct_Sum – t.b. Sep 16 '12 at 16:34

1 Answer

up vote 1 down vote

The answer is not in general, in fact you need to add some conditions, please see this proof 1, I think it can be of help.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.