(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

i have {ej} is an orthonormal basis on a hilbert space

S1 is the 1-dimensional space of e1 and

S2 is the span of vectors ej + 2e(j+1)

eventually i need to show that S1 + S2 is dense in H and also evaluate

S2 for density and closedness

2. Relevant equations

i know the def. of closed, dense, spans, etc...

3. The attempt at a solution

well, i know that i need to show that S1+S2 is dense by showing that its closure = my orthornormal basis. i think S2 is closed but not dense, but can an undense set + a dense set be a dense set?

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# Homework Help: Hilbert spaces

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