cc_master
- 1
- 0
Homework Statement
Give a nontrivial example of an infinite dimensional subspace in l2(R) that is closed. Also find an example of an infinite dimensional subspace of l2(R) that is not closed. Repeat the same two questions for L2(R).
The Attempt at a Solution
To my understanding, l2 is the space of square summable sequences and L2 is the space of square integrable functions. So basically we need to get finite sums / finite integrals to be in l2/L2.
For l2 I'm thinking of the set of sequences { 1/n^p : n, p is N }. I guess my problem is I don't really know if that is "infinite dimensional" and if it is closed or not.
Then for L2 I was thinking of the normal distribution because I know the area under it is finite. Again though, I'm not sure if it is infinite dimensional or closed.